Browsing by Author "Mustafayev, H. S."

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Almost Periodic Functionals on Some Class of Banach Algebras
(Rocky Mt Math Consortium, 2006) Mustafayev, H. S.
In this paper we study the question of characterizing almost periodic functionals on some class of Banach algebras. Some related problems are also discussed.
The Banach Algebras Generated by Representations of Abelian Semigroups
(Springer Wien, 2012) Mustafayev, H. S.
Let S be a suitable subsemigroup of a locally compact abelian group. We consider the class of Banach algebras A for which there exists a continuous homomorphism omega : L (1) (S) -> A with dense range. We study the behavior of the radical in such algebras. As an application, we present some results concerning the structure of weakly compact homomorphisms of semigroup algebras.
The Behavior of The Orbits of Power Bounded Operators
(Element, 2014) Mustafayev, H. S.
Let T be a power bounded operator on a Banach space X and let sigma(T) (x) be the local spectrum of T at x is an element of X. In this paper, we study the asymptotic behavior of the orbits {T(n)x : n >= 0} in terms of the local spectrum of T at x.
The Behavior of the Radical of the Algebras Generated by a Semigroup of Operators on Hilbert Space
(theta Foundation, 2007) Mustafayev, H. S.
Let T = {T(t)}(t >= 0) be a continuous semigroup of contractions on a Hilbert space. We define A(T) as the closure of the set {(f) over cap (T) : f is an element of L-1 (R+)} with respect to the operator-norm topology, where (f) over cap (T) = [GRAPHICS] is the Laplace transform of f is an element of L-1 (R+) with respect to the semigroup T. Then, A(T) is a commutative Banach algebra. In this paper, we obtain some connections between the radical of A(T) and the set {R is an element of A(T) : T(t)R --> 0, strongly or in norm, as t --> infinity}. Similar problems for the algebras generated by a discrete semigroup {T-n : n = 0, 1, 2,...} is also discussed, where T is a contraction.
A Class of Banach Algebras Whose Duals Have the Radon-Nikodym Property
(Birkhauser verlag Ag, 2006) Mustafayev, H. S.
Let A be a complex, commutative Banach algebra and let M-A be the structure space of A. Assume that there exists a continuous homomorphism h : L-1(G) -> A with dense range, where L-1(G) is the group algebra of a locally compact abelian group G. The main results of this paper can be summarized as follows: (a) If the dual space A* has the Radon-Nikodym property, then M-A is scattered (i.e., it has no nonempty perfect subset) and A* center dot A = (SPAN) over barM(A). (b) If the algebra A has an identity, then the space A* has the Radon-Nikodym property if and only if A* = (span) over bar M-A. Furthermore, any of these conditions implies that M-A is scattered. Several applications are given.
Difference Inequalities for the Groups and Semigroups of Operators on Banach Spaces
(Springer Basel Ag, 2012) Mustafayev, H. S.
Let T = {T (t)}(t is an element of R) be a sigma(X, F)-continuous group of isometries on a Banach space X with generator A, where sigma(X, F) is an appropriate local convex topology on X induced by functionals from F subset of X*. Let sigma(A)(x) be the local spectrum of A at x is an element of X and r(A)(x) := sup{|lambda| : lambda is an element of sigma(A)(x)}, the local spectral radius of A at x. It is shown that for every x is an element of X and tau is an element of R, parallel to T(tau)x - x parallel to <= vertical bar tau vertical bar r(A)(x) parallel to x parallel to. Moreover if 0 <= tau r(A)(x) <= pi/2, then it holds that parallel to T(tau)x - T(-tau)x parallel to <= 2 sin (tau r(A)(x)) parallel to x parallel to. Asymptotic versions of these results for C-0-semigroup of contractions are also obtained. If T = {T(t)}(t >= 0) is a C-0-semigroup of contractions, then for every x is an element of X and tau >= 0, lim(t ->infinity) parallel to T (t + tau)x - T(t)x parallel to <= tau sup {vertical bar lambda vertical bar is an element of sigma(A)(x) boolean AND iR} parallel to x parallel to. Several applications are given.
Differential Inequalities in Lp-Spaces
(Academic Press inc Elsevier Science, 2014) Mustafayev, H. S.
In this article, we present inequalities related to the continuous representations of one-parameter groups. As an application, we obtain some differential inequalities of Bernstein type in L-p-spaces: We define the spectrum Sigma(f) of f is an element of L-p (R) (1 <= p < infinity), as Sigma(f) = boolean OR sp(B) {f * k} (1/P + 1/Q = 1), k is an element of L-q (R) where sp(B){.} is the Beurling spectrum. It is shown that if tau is an element of R satisfies the condition 0 <= tau sigma < pi, then f' is an element of L-p(R) and parallel to f'parallel to(p) <= sigma/2 sin tau sigma parallel to f(. + tau) - f(. - tau)parallel to(p), where sigma := sup{vertical bar lambda vertical bar: lambda is an element of Sigma(f)}. Some related problems are also discussed. (C) 2013 Elsevier Inc. All rights reserved.
The Essential Spectrum of the Essentially Isometric Operator
(Canadian Mathematical Soc, 2014) Mustafayev, H. S.
Let T be a contraction on a complex, separable, infinite dimensional Hilbert space and let sigma(T) (resp. sigma(e)(T)) be its spectrum (resp. essential spectrum). We assume that T is an essentially isometric operator; that is, I-H - T* T is compact. We show that if D\sigma T(T) not equal phi, then for every f from the disc-algebra sigma(e)( f(T)) = f( sigma(e)(T)), where D is the open unit disc. In addition, if T lies in the class C-0. boolean OR C-.0, then sigma(e)( f(T)) = f( sigma(T) boolean AND Gamma), where Gamma is the unit circle. Some related problems are also discussed.
Growth Conditions for Operators With Smallest Spectrum
(Cambridge Univ Press, 2015) Mustafayev, H. S.
Let A be an invertible operator on a complex Banach space X. For a given alpha >= 0, we define the class D-A(alpha) (Z) (resp. D-A(alpha) (Z(+))) of all bounded linear operators T on X for which there exists a constant C-T > 0, such that parallel to A(n)TA(-n)parallel to <= C-T ( 1 + vertical bar n vertical bar)(alpha), for all n is an element of Z ( resp. n is an element of Z(+)). We present a complete description of the class D-A(alpha) (Z) in the case when the spectrum of A is real or is a singleton. If T is an element of D-A (Z) (= D-A(0) (Z)), some estimates for the norm of AT - TA are obtained. Some results for the class D-A(alpha) (Z(+)) are also given.
Mixing Type Theorems for One-Parameter Semigroups of Operators
(Springer, 2016) Mustafayev, H. S.
In this paper, we present some results concerning strong and weak mixing properties of continuous one-parameter semigroups of operators on Banach spaces. We study also some stability problems for continuous one-parameter semigroups on Hilbert spaces. Some related problems are also discussed.
The Norm Spectrum in Certain Classes of Commutative Banach Algebras
(Ars Polona-ruch, 2011) Mustafayev, H. S.
Let A be a commutative Banach algebra and let Sigma(A) be its structure space. The norm spectrum sigma(f) of the functional f is an element of A* is defined by sigma(f) = ({f . a : a is an element of A}) over bar boolean AND Sigma(A), where f . a is the functional on A defined by < f . a, b > = < f, ab >, b is an element of A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.
Semisimplicity of Some Class of Operator Algebras on Banach Space
(Birkhauser verlag Ag, 2007) Mustafayev, H. S.
Let G be a locally compact abelian group and let T = {T(9)}(g is an element of G) be a representation of G by means of isometries on a Banach space. We define W-T as the closure with respect to the weak operator topology of the set {f (T) : f is an element of L-1 (G)}, where f (T) f(G) f (g)T (g) dg is the Fourier transform of f G L' (G) with respect to the group T. Then WT is a commutative Banach algebra. In this paper we study semisimlicity problem for such algebras. The main result is that if the Arveson spectrum sp (T) of T is scattered (i.e. it does not contain a nonempty perfect subset) then the algebra WT is semisimple. Some related problems are also discussed.