Related papers: Triangle inequalities for the operator symmetric m…

Truncated Toeplitz operators and their asymmetric versions are studied in the context of the Hardy space $H^p$ of the half-plane for $1<p<\infty$. It is shown that they are equivalent after extension to $2 \times 2$ matricial Toeplitz…

In this paper, we study the existence of solutions of some kinds of operator equations via operator inequalities. First, we investigate characterizations of operator order $A\geqslant B >0$ and chaotic operator order log $A \geqslant$ log…

Let $x=a+ib$ be a complex number, so we have the following inequality $$(1/\sqrt{2})|a+b|\leq |x|\leq |a|+|b|$$ We give an operator version of above inequality. Also we obtain some results for normal operators.

We study the action of symmetric PDO on the module of anti-symmetric functions in $z_1, \dots, z_k$. We show that over the Weyl algebra of the elementary symmetric functions, this module is simple.

We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities.

This is the second half of a two-part series studying tensor categories of unitary vertex operator algebras from a unitary point of view.

We prove several versions of reverse triangle inequality in Hilbert $C^*$-modules. We show that if $e_1, ..., e_m$ are vectors in a Hilbert module ${\mathfrak X}$ over a $C^*$-algebra ${\mathfrak A}$ with unit 1 such that $<e_i,e_j>=0…

In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…

We investigate some modal operators of necessity and possibility in the context of meet-complemented (not necessarily distributive) lattices. We proceed in stages. We compare our operators with others.

We use a result of Barron, Dong and Mason to give a natural isomorphism between the category of twisted modules and the category of quasi-modules of a certain type for a general vertex operator algebra.

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights.…

We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators…

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…

We systematically study how properties of abstract operator systems help classifying linear matrix inequality definitions of sets. Our main focus is on polyhedral cones, the 3-dimensional Lorentz cone, where we can completely describe all…

In this article, we developed a series of new inequalities involving the $q$-numerical radius for operators and $2\times 2$ operator matrices. These inequalities serve to establish both lower and upper bounds for the $q$-numerical radius of…

In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for $s$-convex function. We also give an application to the order preserving power inequality of three variables and find a…

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…

Examples of operator algebras with involution include the operator $*$-algebras occurring in noncommutative differential geometry studied recently by Mesland, Kaad, Lesch, and others, several classical function algebras, triangular matrix…

We provide a brief survey of a certain algebra of operators on symmetric polynomials, and collect a number of previously known results in the field.

Some Gr\"{u}ss type inequalities in semi-inner product modules over $C^*$-algebras and $H^*$-algebras for $n$-tuples of vectors are established. Also we give their natural applications for the approximation of the discrete Fourier and the…