Related papers: A new class of function spaces generalizing the Ar…

We use properties of the sequences of zeros of certain spaces of analytic functions in the unit disc $\mathbb D$ to study the question of characterizing the weighted superposition operators which map one of these spaces into another. We…

Multivariate quasi-projection operators $Q_j(f,\varphi, \widetilde{\varphi})$, associated with a function $\varphi$ and a distribution/function $\widetilde{\varphi}$, are considered. The function $\varphi$ is supposed to satisfy the…

If $\phi$ is a submeasure satisfying an appropriate lower estimate we give a quantitative result on the total mass of a measure $\mu$ satisfying $0\le\mu\le\phi.$ We give a dual result for supermeasures and then use these results to…

Inspired by the recent work of Cascales et al., we introduce a generalized concept of ACK structure on Banach spaces. Using this property, which we call by the quasi-ACK structure, we are able to extend known universal properties on range…

The main purpose of this paper is to introduce the notion of an asymptotically almost periodic ultradistribution and asymptotically almost automorphic ultradistribution with values in a Banach space, as well as to further analyze the…

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…

We extend to a functional setting the concept of quermassintegrals, well-known within the Minkowski theory of convex bodies. We work in the class of quasi-concave functions defined on the Euclidean space, and with the hierarchy of their…

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…

We study unitarity of the induced representations from coisotropic quantum subgroups which were introduced in math.QA/9804138. We define a real structure on coisotropic subgroups which determines an involution on the homogeneous space. We…

It is shown that if the Deddens algebra ${\mathcal D}_T$ associated with a quasinilpotent operator $T$ on a complex Banach space is closed and localizing then $T$ has a nontrivial closed hyperinvariant subspace.

For a general set transformation ${\cal R}$ between two measure spaces, we define the rearrangement of a measurable function by means of the Layer's cake formula. We study some functional properties of the Lorentz spaces defined in terms of…

We investigate the structure of the commutative Banach algebra formed as the direct sum of integrable radial functions on the disc and the radial operators on the Bergman space, endowed with the convolution from quantum harmonic analysis as…

We construct a nonseparable Banach space $\mathcal X$ (actually, of density continuum) such that any uncountable subset $\mathcal Y$ of the unit sphere of $\mathcal X$ contains uncountably many points distant by less than $1$ (in fact, by…

Let ${\mathcal A}$ be a Banach algebra and let $\varphi $ be a non-zero character on ${\mathcal A}$. Suppose that ${\mathcal A}_M$ is the closure of the faithful Banach algebra ${\mathcal A}$ in the multiplier norm. In this paper,…

In this article, we present a formalization of spherically complete spaces, which is a fundamental notion in non-archimedean functional analysis. This work includes the equivalent definitions of spherically complete spaces, their basic…

We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach valued functors and, in particular, prove the existence of an exponential map for…

In classical analysis, the relationship between continuity and Riemann integrability is an intimate one: a continuous function on a closed and bounded interval is always Riemann integrable whereas a Riemann integrable function is continuous…

A motivation comes from {\em M. Ismail and et al.: A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77--84} to study a generalization of close-to-convex functions by means of a $q$-analog of a difference…

We present and study some transfinite versions of (almost isometric) ideals in Banach spaces. As these notions are closely related with Lindenstrauss and Gurari\u{\i} spaces respectively, we will present a similar characterization for…

We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost…