Related papers: Some problems in functional analysis inspired by H…

The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…

In the multicentric calculus one takes a polynomial with simple roots as a new global variable and replaces scalar functions {\varphi} by functions f taking values in C^d with d the degree of the polynomial leading to an efficient…

We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach…

The problems connected with equivalent norms lie at the heart of Banach space theory. This is a short survey on some recent as well as classical results and open problems in renormings of Banach spaces.

The Haraux function is an important tool in monotone operator theory and its applications. One of its salient properties for a maximally monotone operator is to be valued in $[0,+\infty]$ and to vanish only on the graph of the operator.…

In this survey, we consider Banach spaces of analytic functions in one and several complex variables for which: (i) polynomials are dense, (ii) point-evaluations on the domain are bounded linear functionals, and (iii) the shift operator…

A quadrilateral inequality established by C. Sch\"otz in the context of Hilbert spaces is extended to the framework of Banach spaces. Our approach is based on the majorization theory and a substitute for the parallelogram law associated…

Metric regularity has emerged during last 2-3 decades as one of the central concepts of variational analysis. The roots of this concept go back to a circle of fundamental regularity ideas of classical analysis embodied in such results as…

Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis.…

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…

In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…

We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order…

This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…

Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…

We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods…

Since its invention in 1979, the Feichtinger algebra has become a very useful Banach space of functions with applications in time-frequency analysis, the theory of pseudo-differential operators and several other topics. It is easily defined…

The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz (1982). Previously, J. Lindenstrauss (1966) studied similar versions of this notion in the context of non separable reflexive Banach…

We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…

We use techniques of proof mining to obtain a computable and uniform rate of metastability (in the sense of Tao) for the mean ergodic theorem for a finite number of commuting linear contractive operators on a uniformly convex Banach space.