Related papers: Semi-inner product and angles in Schatten ideals
Ideals are one of the main topics of interest to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be…
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is,…
In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime…
Given an ample action of an inverse semigroup on a locally compact and Hausdorff topological space, we study the ideal structure of the crossed product algebra associated with it. By developing a theory of induced ideals, we manage to prove…
We present a new approach to define a suitable integral for functions with values in quasi-Banach spaces. The integrals of Bochner and Riemann have deficiencies in the non-locally convex setting. The study of an integral for $p$-Banach…
We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…
Let $S\subseteq \mathbb N^p$ be a semigroup, any $P\subseteq S$ is an ideal of $S$ if $P+S\subseteq P$, and an $I(S)$-semigroup is the affine semigroup $P\cup \{0\}$, with $P$ an ideal of $S$. We characterise the $I(S)$-semigroups and the…
We adopt a new perspective on the tensor product of arbitrary semi-lattices. Our basic construction exploits a description of semi-lattices in terms of bi-extensional Chu spaces associated to a target space defined to be the boolean domain.…
This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…
We study operators of the form X+Y where Y has a finite p-th Schatten norm (p<2), and X is self-adjoint and of Hilbert-Schmidt class. Our study is based on new theorems on zero distribution of entire functions of finite order.
We introduce the notions of pointwise almost h-slant submanifolds and pointwise almost h-semi-slant submanifolds as a generalization of slant submanifolds, pointwise slant submanifolds, semi-slant submanifolds, and pointwise semi-slant…
We study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As an application of the present study, some distance formulae are…
We introduce the notion of intrinsic subspaces of linear and affine pair geometries, which generalizes the one of projective subspaces of projective spaces. We prove that, when the affine pair geometry is the projective geometry of a Lie…
In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…
The optimal 2-uniform convexity of Schatten classes $S_p, 1<p\le 2$ was first proved by Ball, Carlen and Lieb \cite{BCL94}. In this note we revisit this result using multiple operator integrals and generalized monotone metrics in quantum…
This is an attempt to model ambient space as a three-dimensional real affine space with a distinguished group of automorphisms containing the translations and acting freely and transitively on pairs consisting of a half-plane together with…
A new inequality between angles in inner product spaces is formulated and proved. It leads directly to a concise statement and proof of the generalized Wielandt inequality, including a simple description of all cases of equality. As a…
We identify the smooth points of $L^1(\mu,X)$, and provide some necessary and sufficient conditions for left and right symmetry of points with respect to Birkhoff-James orthogonality in $L^p(\mu,X), 1\leq p<\infty$, where $\mu$ is any…
The study of Schatten classes has a long tradition in geometric functional analysis and related fields. In this paper we study a variety of geometric and probabilistic aspects of finite-dimensional Schatten classes of not necessarily square…
Fix a prime number $p$ and let $E/F$ be a CM extension of number fields in which $p$ splits relatively. Let $\pi$ be an automorphic representation of a quasi-split unitary group of even rank with respect to $E/F$ such that $\pi$ is ordinary…