Related papers: A Certain p-Adic Spectral Theorem

Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain…

We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…

We study the spectral synthesis for the Banach *-algebra $A\oop B$, the operator space projective tensor product of $C^*$-algebras $A$ and $B$. It is shown that if $A$ or $B$ has finitely many closed ideals, then $A\oop B$ obeys spectral…

In this note we study the endomorphisms of certain Banach algebras of infinitely differentiable functions on compact plane sets, associated with weight sequences M. These algebras were originally studied by Dales, Davie and McClure. In a…

We discuss an "almost" version of Auslander regularity and use it to prove the Auslander regularity of various Banach algebras over non-discretely valued fields appearing naturally in $p$-adic locally analytic representation theory:…

We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.

Let $K$ be a $p$-adic field. We continue to develop the theory of rigid analytic $p$-divisible groups over $K$. For example, we explain how to find back the category of Banach-Colmez spaces from rigid analytic $p$-divisible groups "in…

We present new additive results for the pseudo core inverse in a Banach algebra with involution. The necessary and sufficient conditions under which the sum of two pseudo core invertible elements in Banach *-algebra is pseudo core…

We use an extension to the infinite dimension of the rank theorem of the differential calculus to establish a Karush-Huhn-Tucker theorem for optimization problems in Banach spaces. We provide an application to variational problems on…

In this paper, we investigate the theory of $R$-brackets, Baxter brackets and Nijenhuis brackets in the Banach setting, in particular in relation with Banach Poisson-Lie groups. The notion of Banach Lie-Poisson space with respect to an…

Several basic properties of the Drazin spectrum in Banach algebras will be studied. As an application, some results on meromorphic Banach space operators will be obtained.

Character inner amenability for certain class of Banach algebras consist of projective tensor product $A\hat{\otimes}B$, Lau product $A\times_\theta B$ and module extension $A\oplus X$ are investigated. Some illuminating examples are also…

A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…

We develop a systematic functional-analytic framework for Hom--Lie Banach algebras, introducing bounded $\alpha$-twisted derivations and almost periodic elements. Under natural continuity and compactness assumptions, we establish a complete…

We prove an analogue of the Cauchy integral theorem for hyperholomorphic functions given in three-dimensional domains with non piece-smooth boundaries and taking values in an arbitrary finite-dimensional commutative associative Banach…

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the…

Let $X$ be a Banach space, $A\in B(X)$ and $M$ be an invariant subspace of $A$. We present an alternative proof that, if the spectrum of the restriction of $A$ to $M$ contains a point that is in any given hole in the spectrum of $A$, then…

We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\mathbb{Z})$ of $p$-pseudofunctions on $\mathbb{Z}$, the…

We prove that finite-spectrum representations of compact quantum groups either in unital $C^*$-algebras $A$ or on Banach spaces $E$ exhibit the same Banach-space-modeled differential-geometric structure as their classical analogues: (a)…

We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space $X$. This is done by finite dimensional approximation. In particular we prove…