Search results for "Functional analysis"

Continuous *-homomorphisms of Banach Partial *-algebras

2007

We continue the study of Banach partial *-algebras, in particular the question of the interplay between *-homomorphisms and biweights. Two special types of objects are introduced, namely, relatively bounded biweights and Banach partial *-algebras satisfying a certain Condition (S), which behave in a more regular way. We also present a systematic construction of Banach partial *-algebras of this type and exhibit several examples.

SOME SPECTRAL PROPERTIES OF MULTIPLIERS ON SEMI-PRIME BANACH ALGEBRAS

1995

Abstract We extend to arbitrary semi-prime Banach algebras some results of spectral theory and Fredholm theory obtained in [1] and [2] for multipliers defined in commutative semi-simple Banach algebras.

A probabilistic Weitzenböck formula on Riemannian path space

2000

Banach elements and spectrum in Banach quasi *-algebras

2006

A normal Banach quasi -algebra (X;A_0) has a distinguished Banach - algebra X_b consisting of bounded elements of X. The latter -algebra is shown to coincide with the set of elements of X having fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).

Spectrum and Pseudo-Spectrum

2019

In this book all Hilbert spaces will be assumed to separable for simplicity. In this section we review some basic definitions and properties; we refer to Kato (Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer, New York, 1966), Reed and Simon (Methods of modern mathematical physics. I. Functional analysis, 2nd edn. Academic, New York, 1980; Methods of modern mathematical physics. II. Fourier analysis, self adjointness. Academic, New York, 1975; Methods of modern mathematical physics. IV. Analysis of operators. Academic, New York, 1978), Riesz and Sz.-Nagy (Lecons d’analyse fonctionnelle, Quatrieme edition. Academie des Sciences d…

Crystalline-state reaction with allosteric effect in spin-crossover, interpenetrated networks with magnetic and optical bistability.

2003

A net change: A fully reversible ligand substitution involving coordination/ uncoordination of gaseous water and pyrimidine induces the repetitive allosteric transformation of three interpenetrated nets into a single three-dimensional net. The transformation does not affect the crystallinity of the sample but alters significantly the spin-crossover transition; the compound shows magnetic and chromatic bistability (see picture).

Gabor systems and almost periodic functions

2017

Abstract Inspired by results of Kim and Ron, given a Gabor frame in L 2 ( R ) , we determine a non-countable generalized frame for the non-separable space AP 2 ( R ) of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of AP 2 ( R ) are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.

Singular integrals on regular curves in the Heisenberg group

2019

Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \mathbb{H} \, \setminus \, \{0\}, \, n \geq 0.$$ The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel $k(p) = \nabla_{\mathbb{H}} \log \|p\|$. We prove that convolution with $k$, as above, yields an $L^{2}$-bounded operator on regular curves in $\mathbb{H}$. This extends a theorem of G. David to the Heisenberg group. As a corollary of our main result, we infer that all …

Dimension estimates for the boundary of planar Sobolev extension domains

2020

We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.

Jacobian of solutions to the conductivity equation in limited view

2022

Abstract The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the bounda…