相关论文: An inequality for tensor product of positive opera…

We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator…

Tensor product operators on finite dimensional Hilbert spaces are studied. The focus is on bilinear tensor product operators. A tensor product operator on a pair of Hilbert spaces is a maximally general bilinear operator into a target…

On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…

This paper presents a number of Kantorovich type integral inequalities involving tensor products of continuous fields of bounded linear operators on a Hilbert space. Kantorovich type inequality in which the product is replaced by an…

In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The…

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…

We study symmetric and antisymmetric tensor products of Hilbert-space operators, focusing on norms and spectra for some well-known classes favored by function-theoretic operator theorists. We pose many open questions that should interest…

We prove inequalities on symmetric tensor sums of positive definite operators. In particular, we prove multivariable operator inequalities inspired by generalizations to the well-known Hlawka and Popoviciu inequalities. As corollaries, we…

A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…

We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…

We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results…

A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…

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.

The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular…

This is a continuation of our previous paper. We consider a certain order-like relation for positive operators on a Hilbert space. This relation is defined by using the Jensen inequality with respect to the square-root function. We show…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.

This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…

We study the concept of frame in tensor product of n-Hilbert spaces as tensor product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship…