Displaying similar documents to “Pointwise multiplication operators on weighted Banach spaces of analytic functions”

Supercyclicity and weighted shifts

Héctor Salas (1999)

Studia Mathematica

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An operator (linear and continuous) in a Fréchet space is hypercyclic if there exists a vector whose orbit under the operator is dense. If the scalar multiples of the elements in the orbit are dense, the operator is supercyclic. We give, for Fréchet space operators, a Supercyclicity Criterion reminiscent of the Hypercyclicity Criterion. We characterize the supercyclic bilateral weighted shifts in terms of their weight sequences. As a consequence, we show that a bilateral weighted shift...

Mapping properties of integral averaging operators

H. Heinig, G. Sinnamon (1998)

Studia Mathematica

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Characterizations are obtained for those pairs of weight functions u and v for which the operators T f ( x ) = ʃ a ( x ) b ( x ) f ( t ) d t with a and b certain non-negative functions are bounded from L u p ( 0 , ∞ ) to L v q ( 0 , ∞ ) , 0 < p,q < ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.

Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight

A. Böttcher, M. Seybold (2000)

Studia Mathematica

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The discrete Wiener-Hopf operator generated by a function a ( e i θ ) with the Fourier series ∑ n ∈ ℤ a n e i n θ is the operator T(a) induced by the Toeplitz matrix ( a j - k ) j , k = 0 ∞ on some weighted sequence space l p ( ℤ + , w ) . We assume that w satisfies the Muckenhoupt A p condition and that a is a piecewise continuous function subject to some natural multiplier condition. The last condition is in particular satisfied if a is of bounded variation. Our main result is a Fredholm criterion and an index formula for T(a). It implies that the...

Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems

Sen Huang (1995)

Studia Mathematica

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Let A be a closed linear operator in a Banach space E. In the study of the nth-order abstract Cauchy problem u ( n ) ( t ) = A u ( t ) , t ∈ ℝ, one is led to considering the linear Volterra equation (AVE) u ( t ) = p ( t ) + A ʃ 0 t a ( t - s ) u ( s ) d s , t ∈ ℝ, where a ( · ) ∈ L l o c 1 ( ℝ ) and p(·) is a vector-valued polynomial of the form p ( t ) = ∑ j = 0 n 1 / ( j ! ) x j t j for some elements x j ∈ E . We describe the spectral properties of the operator A through the existence of slowly growing solutions of the (AVE). The main tool is the notion of Carleman spectrum of a vector-valued function. Moreover, an extension...

On the shift operators.

Aggour, M.M. (1996)

International Journal of Mathematics and Mathematical Sciences

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Spectra of weighted composition operators on algebras of analytic functions on Banach spaces

Cheng Yuan, Ze-Hua Zhou (2011)

Czechoslovak Mathematical Journal

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Let E be a complex Banach space, with the unit ball B E . We study the spectrum of a bounded weighted composition operator u C ϕ on H ∞ ( B E ) determined by an analytic symbol ϕ with a fixed point in B E such that ϕ ( B E ) is a relatively compact subset of E , where u is an analytic function on B E .