Browsing by Author "Mustafayev, Heybetkulu"

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The Behavior of Iterates of Multipliers in Commutative Banach Algebras
(Polish Acad Sciences inst Mathematics-impan, 2022) Mustafayev, Heybetkulu; Topal, (Van) Hayri
Let A be a complex, commutative, and semisimple Banach algebra and let T be a power bounded multiplier on A. We prove a Katznelson-Tzafriri type theorem for T. As an application, we give some results concerning convergence of the sequence {T(n)a} (a is an element of A). Some related problems are also discussed.
Compact Homomorphisms of Regular Banach Algebras
(Wiley-v C H verlag Gmbh, 2011) Mustafayev, Heybetkulu; Temel, Cesim
Let A be a complex commutative Banach algebra and let M-A be the maximal ideal space of A. We say that A has the bounded separating property if there exists a constant C > 0 such that for every two distinct points phi(1), phi(2). M-A, there is an element a is an element of A for which (a) over cap (phi(1)) = 1, (a) over cap (phi(2)) = 0 and parallel to a parallel to <= C, where (a) over cap is the Gelfand transform of a is an element of A. We show that if A is a strongly regular Banach algebra with the bounded separating property, then every compact homomorphism from A into another Banach algebra is of finite dimensional range. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Convergence of Iterates of Convolution Operators in Lp Spaces
(Elsevier Science Bv, 2019) Mustafayev, Heybetkulu
Let G be a locally compact abelian group and let M (G) be the measure algebra of G. Assume that mu is an element of M (G) is power bounded, that is, sup(n >= 0) parallel to mu(n)parallel to(1) < infinity. This paper is concerned mainly with finding necessary and sufficient conditions for strong convergence of iterates of the convolution operators T(mu)f : = mu * f in L-P (G) (1 <= p < infinity) spaces. Some related problems are also discussed. (C) 2019 Elsevier Masson SAS. All rights reserved.
Dissipative Operators on Banach Spaces
(Academic Press inc Elsevier Science, 2007) Mustafayev, Heybetkulu
A bounded linear operator T on a Banach space is said to be dissipative if parallel to e(tT)parallel to <= 1 for all t >= 0. We show that if T is a dissipative operator on a Banach space, then: (a)lim(t)->infinity parallel to e(tT) T parallel to = {vertical bar lambda vertical bar: lambda epsilon sigma (T) boolean AND i R} (b) If sigma (T) boolean AND i R is contained in [-i pi/2, i pi/2], then [GRAPHICS] Some related problems are also discussed. (c) 2007 Elsevier Inc. All rights reserved.
Distance Formulas in Group Algebras
(Elsevier France-editions Scientifiques Medicales Elsevier, 2016) Mustafayev, Heybetkulu
Let G be a locally compact amenable group, A (G) and B (G) be the Fourier and the Fourier-Stieltjes algebra of G, respectively. For a given u is an element of B (G), let epsilon(u):={g is an element of G : vertical bar u(g)vertical bar = 1}. The main result of this paper particularly states that if parallel to u parallel to(B(G)) <= 1 and <(u(epsilon(u)))over bar>is countable (in particular, if epsilon(u) is compact and scattered), then lim(n ->infinity) parallel to u(n)v parallel to(A(G)) = dist (v, I-epsilon u ),for all v is an element of A (G), where I-epsilon u = {v is an element of A (G) : v(g = 0, for all g is an element of epsilon(u) )}. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Ergodic Properties of Convolution Operators in Group Algebras
(Ars Polona-ruch, 2021) Mustafayev, Heybetkulu; Topal, Hayri
Let G be a locally compact abelian group and let L-1 (G) and M(G) be respectively the group algebra and the convolution measure algebra of G. For mu is an element of M(G), let T(mu)f = mu * f be the convolution operator on L-1(G). A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0)parallel to mu(n)parallel to(1) < infinity, where mu(n) denotes the nth convolution power of mu. We study some ergodic properties of the convolution operator T-mu, in the case when mu is power bounded. We also present some results concerning almost everywhere convergence of the sequence {T(mu)(n)f} in L-1 (G).
Estimate Multiplicity of Some Operators
(2013) Arslan, Cihan; Mustafayev, Heybetkulu
Bu çalışmada, X ayrılabilir bir kompleks Banach uzayında bazı sınıf lineer ve sınırlı operatörlerin katlılığını incelemiştir. Ayrıca bu tezde C(r) ve A(D)-disk cebirinde çarpma operatörünün katlılığını da incelemiştir. Eğer T operatörü A(D) de bir çarpma operatörü ise m(T^n)=n olduğunu gösterilmiştir.
Growth Conditions for Conjugation Orbits of Operators on Banach Spaces
(theta Foundation, 2015) Mustafayev, Heybetkulu
Let A be an invertible bounded linear operator on a complex Banach space X. With connection to the Deddens algebras, for a given k is an element of N, we define the class D-A(k) of all bounded linear operators T on X for which the conjugation orbits {A(n)TA(-n)}(n is an element of z) satisfies some growth conditions. We present a complete description of the class D-A(k) in the case when the spectrum of A is positive. Individual versions of Katznelson-Tzafriri theorem and their applications to the Deddens algebras are given. The Hille-Yosida space is used to obtain local quantitative results related to the Katznelson-Tzafriri theorem. Some related problems are also discussed.
Local Spectrum, Local Spectral Radius, and Growth Conditions
(Springer Wien, 2021) Mustafayev, Heybetkulu
Let X be a complex Banach space and x is an element of X. Assume that a bounded linear operator parallel to etT(x)parallel to <= C-x (">1+vertical bar t vertical bar)(alpha) (alpha >= 0), for all t is an element of R and for some constant Cx > 0. For the function f from the Beurling algebra L omega 1 with the weight omega(t) (>1+t(alpha)) we can define an element in X, denoted by xf, which integrates etTx with respect to f. We present a complete description of the elements xf in the case when the local spectrum of T at x consists of one point. In the case 0 <=alpha<1, some estimates for the norm of Tx via the local spectral radius of T at x are obtained. Some applications of these results are also given.
Mean Ergodic Theorems for Multipliers on Banach Algebras
(Springer Birkhauser, 2019) Mustafayev, Heybetkulu
Let A be a complex commutative semisimple Banach algebra. In this paper, we study some ergodic properties of Cesaro bounded multipliers on A. The results are linked to the sets of synthesis and the main applications are concerned with Fourier and Fourier-Stieltjes algebras on locally compact groups. We study also the structure of ideals associated with multipliers of A and A-invariant projections of the dual space of A. Some related problems are also discussed.
Mean Ergodic Theorems for Power Bounded Measures
(Academic Press inc Elsevier Science, 2021) Mustafayev, Heybetkulu; Sevli, Hamdullah
Let G be a locally compact abelian group and let M(G) be the convolution measure algebra of G. A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0) parallel to mu(n)parallel to(1) < infinity, where mu(n) denotes nth convolution power of mu. We show that if mu is an element of M(G) is power bounded and A = [a(n,k)](n,k=0)(infinity) is a strongly regular matrix, then the limit lim(n ->infinity) Sigma(infinity)(k=0) a(n,k) mu(k) exists in the weak* topology of M(G) and is equal to the idempotent measure theta, where (theta) over cap = 1(int)F(mu). Here, (theta) over cap is the Fourier-Stieltjes transform of theta, F-mu :={gamma is an element of Gamma : (mu) over cap(gamma) = 1}, and 1(int) F-mu is the characteristic function of int F-mu. Some applications are also given. (C) 2021 Elsevier Inc. All rights reserved.
A Note on the Kawada-Ito Theorem
(Elsevier, 2022) Mustafayev, Heybetkulu
A probability measure mu on a locally compact group G is said to be adapted if the support of mu generates a dense subgroup of G. A classical Kawada-Ito theorem asserts that if mu is an adapted measure on a compact metrizable group G, then the sequence of probability measures {1/n Sigma(n=1)(k=0) mu(k)}(n=1)(infinity) weak* converges to the Haar measure on G. In this note, we present a new proof of Kawada-Ito theorem. Also, we show that metrizability condition in the Kawada-Ito theorem can be removed. Some applications are also given. (C) 2021 Elsevier B.V. All rights reserved.
On Operator Equations
(2013) Gürbüz, Ceren; Mustafayev, Heybetkulu
Bu çalışmada, operatör denklemler incelenmiştir. Bilim ve mühendislikte birçok problem için soyut model teşkil eden operatör denklemlerin hangi şartlar altında çözüme sahip olduğu, çözümün inşası ile ilgili temel tanım ve teoremler ifade edilmiştir.
On the Convergence of Iterates of Convolution Operators in Banach Spaces
(Matematisk inst, 2020) Mustafayev, Heybetkulu
Let G be a locally compact abelian group and let M(G) be the measure algebra of G. A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0) parallel to mu(n)parallel to(1) < infinity. Let T = {T-g : g is an element of G} be a bounded and continuous representation of G on a Banach space X. For any mu is an element of M(G), there is a bounded linear operator on X associated with mu, denoted by T-mu, which integrates T-g with respect to mu. In this paper, we study norm and almost everywhere behavior of the sequences {T-mu(n) x} (x is an element of X) in the case when mu, is power bounded. Some related problems are also discussed.
Some Convergence Theorems for Multipliers on Commutative Banach Algebras
(Univ Szeged, Bolyai institute, 2018) Mustafayev, Heybetkulu
Let A be a complex commutative semisimple Banach algebra and let T be a power bounded multiplier of A. This paper is concerned with finding necessary and sufficient conditions for the convergence of the sequence {T-n a} (a is an element of A) in A. Some related problems are also discussed.
Some Convergence Theorems for Operator Sequences
(Springer Basel Ag, 2020) Mustafayev, Heybetkulu
Let A, T, and B be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences {A(n)TB(n)} and {1/n Sigma(n-1)(i=0) A(i)TB(i)}. These results are applied to the Toeplitz, composition, and model operators. Some related problems are also discussed.
Some Convergence Theorems in Fourier Algebras
(Cambridge Univ Press, 2017) Mustafayev, Heybetkulu
Let G be a locally compact amenable group and A(G) and B(G) be the Fourier and the Fourier-Stieltjes algebras of G; respectively. For a power bounded element u of B(G), let epsilon(u) : = {g is an element of G : |u(g)| = 1}. We prove some convergence theorems for iterates of multipliers in Fourier algebras. (a) If parallel to u parallel to(B(G)) <= 1, then lim(n ->infinity) parallel to u(n)v parallel to(A(G)) = dist(v, I epsilon(u)) for v is an element of A(G), where I-epsilon u = {v is an element of A(G) : v(epsilon(u)) = {0}}. (b) The sequence {u(n)v}(n is an element of N) converges for every v is an element of A(G) if and only if epsilon(u) is clopen and u(epsilon(u)) = {1}. (c) If the sequence {u(n)v}(n is an element of N) converges weakly in A(G) for some v is an element of A(G), then it converges strongly.
Some Ergodic Properties of Multipliers on Commutative Banach Algebras
(Tubitak Scientific & Technological Research Council Turkey, 2019) Mustafayev, Heybetkulu; Topal, Hayri
A commutative semisimple regular Banach algebra Sigma(A) with the Gelfand space Sigma(A) is called a Ditkin algebra if each point of Sigma(A) boolean OR {infinity} is a set of synthesis for A. Generalizing the Choquet-Deny theorem, it is shown that if T is a multiplier of a Ditkin algebra A, then {phi is an element of A* : T* phi = phi} is finite dimensional if and only if card F-T is finite, where F-T = {gamma is an element of Sigma(A) : (T) over cap (gamma) = 1} and (T) over cap is the Helgason-Wang representation of T.