Browsing by Author "Mustafayev, HS"

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    The Banach Algebra Generated by a Contraction
    (Amer Mathematical Soc, 2006) Mustafayev, HS
    Let T be a contraction on a Banach space and AT the Banach algebra generated by T. Let sigma(u)(T) be the unitary spectrum ( i. e., the intersection of sigma(T) with the unit circle) of T. We prove the following theorem of Katznelson-Tzafriri type: If sigma(u)(T) is at most countable, then the Gelfand transform of R is an element of A(T) vanishes on sigma(u)(T) if and only if lim(n ->infinity) parallel to(TR)-R-n parallel to = 0.
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    Compact Elements of the Algebras Pmp(G) and Pfp(G) of a Locally Compact Group
    (Akademiai Kiado, 2003) Mustafayev, HS
    Compact and weakly compact elements of the group algebra L-1(G) of a locally compact group G, have been considered by a number of authors. In these investigations it has been shown that, if G is non-compact, then the only weakly compact element of L-1(G) is zero. Conversely, if G is compact, then every element of L-1(G) is compact. For 1 < p < infinity, let PMp (G) and PFp (G) denote the closure of L-1(G), considered as an algebra of convolution operators on L-p(G), with respect to the weak operator topology and the norm topology, respectively, in B((LP)-P-p(G)), the bounded linear operators on LP(G). We study the question of characterizing compact and weakly compact elements of the algebras PMp(G) and PFp(G).