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In this article, we present a new subadditivity behavior of convex and concave functions, when applied to Hilbert space operators. For example, under suitable assumptions on the spectrum of the positive operators $A$ and $B$, we prove that…

We develop upper and lower bounds for the numerical radius of $2\times 2$ off-diagonal operator matrices, which generalize and improve on the existing ones. We also show that if $A$ is a bounded linear operator on a complex Hilbert space…

An operator $T$ on a Hilbert space is called half-centered if the sequence $T^{*}T,(T^{*})^{2}T^{2},...$ consists of mutually commuting operators. It is a subclass of the well-studied centered operators. In this paper we give a condition…

This paper provides new necessary and sufficient conditions for the solvability to the operator equations $ AX-XB=C$ and $AX-YB=C,$ where $A $ and $B $ are group invertible operators defined on an infinite dimensional Hilbert space. In…

In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…

Given Hilbert space operators $P,T\in B(\H), P\geq 0$ invertible, $T$ is $(m,P)-$ expansive (resp., $(m,P)-$ isometric) for some positive integer $m$ if…

Maximally monotone operators play important roles in optimization, variational analysis and differential equations. Finding zeros of maximally monotone operators has been a central topic. In a Hilbert space, we show that most resolvents are…

We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.

Let $\mathcal{H}$ be a complex, separable Hilbert space (of finite or infinite dimension), and let $\mathcal{U}(\mathcal{H})$ denote the group of unitary operators on $\mathcal{H}$. A symmetry is, by definition, a unitary operator $J$ with…

(1) Let $A$ be an operator on a space ${\cal H}$ of even finite dimension. Then for some decomposition ${\cal H}={\cal F}\oplus{\cal F}^{\perp}$, the compressions of $A$ onto ${\cal F}$ and ${\cal F}^{\perp}$ are unitarily equivalent. (2)…

In this article, we discuss necessary condition of conditional dilation for both completely non-unitary (c.n.u) $\Gamma_{n}$-contractions and c.n.u $\mathbb E$-contractions. Consider two tuples, $(A_1, \dots, A_{n-1})$ and $(B_1, \dots,…

A bounded linear operator $A$ on a Hilbert space is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. Posinormality of $A$ is equivalent to the inclusion of the range of $A$ in the range of its adjoint $A^*$.…

We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic…

We study the positive-definiteness of a family of $L^2(\mathbf{R})$ integral operators with kernel $K_{t, a}(x, y) = (1 + (x - y)^2 + a(x^2 + y^2)^t)^{-1}$, with $t > 0$ and $a > 0$. When $0 < t \le 1$, the known theory of positive-definite…

We consider positive semidefinite kernels valued in the $*$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of $*$-semigroups. For…

Let $A,B\in B(H)$. In the present paper, we establish simple and interesting facts on when we have $|A||B|=|B||A|$, $|AB|=|A||B|$, $|A\pm B|\leq |A|+|B|$, $||A|-|B||\leq |A\pm B|$ and $\||A|-|B|\|\leq \|A\pm B\|$, where $|\cdot|$ denotes…

We consider light-ray operators $\mathcal{L}_{2n} = \int\mathrm{d} x^+ (x^+)^{2n}T_{++}$, where $x^+$ is a null coordinate and $n$ a positive integer, in QFT in Minkowski spacetime in arbitrary dimensions. These operators are…

Let A be a positive operator in an infinite sigma-finite von Neumann factor M and let B_j be a sequence of positive elements in M. We give sufficient conditions for decomposing A into a sum of elements C_j equivalent to B_j for all j ( C…

Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a…

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…