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Simple examples of bounded domains $D \subset 𝐑^{3}$ are considered for which the presence of peculiar corners and edges in the boundary $δ D$ causes that the double layer potential operator acting on the space $𝒮 (δ D)$ of all continuous functions on $δ D$ can for no value of the parameter $α$ be approximated (in the sub-norm) by means of operators of the form $α I + T$ (where $I$ is the identity operator and $T$ is a compact linear operator) with a deviation less then $| α |$ ; on the other hand, such approximability turns out to be possible for...

Some problems on narrow operators on function spaces

Mikhail Popov, Evgenii Semenov, Diana Vatsek (2014)

Open Mathematics

It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i....

Some properties of endomorphisms of Lipschitz algebras

Herbert Kamowitz, Stephen Scheinberg (1990)

Studia Mathematica

Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator

Anatoliĭ Antonevich, Jürgen Appell, Petr Zabreĭko (1994)

Studia Mathematica

We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.

Some remarks on time-dependent evolution systems in the hyperbolic case

Silvano Delladio (1990)

Rendiconti del Seminario Matematico della Università di Padova

Spaces of D-paraanalytic elements [Book]

D. Przeworska-Rolewicz (1990)

Spaces of multipliers and their preduals for the order multiplication on [0, 1]

Savita Bhatnagar, H. L. Vasudeva (2002)

Colloquium Mathematicae

Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), $L^{p} (I)$ , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise $H o m_{C (I)} (L^{r} (I), L^{p} (I))$ and their preduals.

Spatial numerical range of operators on weighted Hardy spaces.

Abdollahi, Abdolaziz, Heydari, Mohammad Taghi (2011)

International Journal of Mathematics and Mathematical Sciences

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

Cheng Yuan, Ze-Hua Zhou (2011)

Czechoslovak Mathematical Journal

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 $H^{\infty} (B_{E})$ 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 $B_{E}$ .

Spectral approximation of multiplication operators.

Morrison, Kent E. (1995)

The New York Journal of Mathematics [electronic only]

Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces

Ted Eklund, Mikael Lindström, Paweł Mleczko (2016)

Studia Mathematica

The spectra of invertible weighted composition operators $u C_{φ}$ on the Bloch and Dirichlet spaces are studied. In the Bloch case we obtain a complete description of the spectrum when φ is a parabolic or elliptic automorphism of the unit disc. In the case of a hyperbolic automorphism φ, exact expressions for the spectral radii of invertible weighted composition operators acting on the Bloch and Dirichlet spaces are derived.

Statistical approximation by positive linear operators

O. Duman, C. Orhan (2004)

Studia Mathematica

Using A-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function f by means of a sequence Tₙ(f;x) of positive linear operators acting from a weighted space $C_{ϱ ₁}$ into a weighted space $B_{ϱ ₂}$ .

Statistical periodicity of deterministic systems

Andrzej Lasota, James A. Yorke (1986)

Časopis pro pěstování matematiky

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