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Strictly cyclic algebra of operators acting on Banach spaces H p ( β )

Bahmann Yousefi — 2004

Czechoslovak Mathematical Journal

Let { β ( n ) } n = 0 be a sequence of positive numbers and 1 p < . We consider the space H p ( β ) of all power series f ( z ) = n = 0 f ^ ( n ) z n such that n = 0 | f ^ ( n ) | p β ( n ) p < . We investigate strict cyclicity of H p ( β ) , the weakly closed algebra generated by the operator of multiplication by z acting on H p ( β ) , and determine the maximal ideal space, the dual space and the reflexivity of the algebra H p ( β ) . We also give a necessary condition for a composition operator to be bounded on H p ( β ) when H p ( β ) is strictly cyclic.

Numerical range of operators acting on Banach spaces

Khadijeh JahediBahmann Yousefi — 2012

Czechoslovak Mathematical Journal

The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small...

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