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Analyticity of the Spectral Multi-Function in Topological Algebras

Enrico Casadio Tarabusi (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Se f : Ω 𝒰 è un'applicazione olomorfa di un domìnio di in un'algebra topologica che gode di certe proprietà, si dimostra che la multifunzione «spettro» σ f : Ω 2 C è analitica secondo Oka.

Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains

Kazimierz Włodarczyk (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in J * -algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.

Anisotropic Besov spaces and approximation numbers of traces on related fractal sets.

Erika Tamási (2006)

Revista Matemática Complutense

This paper deals with approximation numbers of the compact trace operator of an anisotropic Besov space into some Lp-space,trΓ: Bpps,a (Rn) → Lp(Γ), s > 0, 1 < p < ∞,where Γ is an anisotropic d-set, 0 < d < n. We also prove homogeneity estimates, a homogeneous equivalent norm and the localization property in Bpps,a.

Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii (2007)

Annales de l’institut Fourier

We study spectral properties of transfer operators for diffeomorphisms T : X X on a Riemannian manifold X . Suppose that Ω is an isolated hyperbolic subset for T , with a compact isolating neighborhood V X . We first introduce Banach spaces of distributions supported on V , which are anisotropic versions of the usual space of C p functions C p ( V ) and of the generalized Sobolev spaces W p , t ( V ) , respectively. We then show that the transfer operators associated to  T and a smooth weight g extend boundedly to these spaces, and...

Another approach to characterizations of generalized triangle inequalities in normed spaces

Tamotsu Izumida, Ken-Ichi Mitani, Kichi-Suke Saito (2014)

Open Mathematics

In this paper, we consider a generalized triangle inequality of the following type: x 1 + + x n p x 1 p μ 1 + + x 2 p μ n f o r a l l x 1 , ... , x n X , where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].

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