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The Sandwich Rule for Sequences of Self-Adjoint Operators and Some Applications
In this paper, we mainly deal with sequences of bounded linear operators on Hilbert space. The main result is the so-called squeeze theorem (or...
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On the Invertibility of the Sum of Operators
The primary purpose of this paper is to investigate the question of the invertibility of the sum of operators in the bounded and unbounded setting....
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Generation of relatively uniformly continuous semigroups on vector lattices
We prove a Hille–Yosida type theorem for relatively uniformly continuous positive semigroups on vector lattices. We introduce the notions of...
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An Addendum to a Paper by Li and Zhang
Recently C.-K. Li and F. Zhang gave a short proof of S.W. Drury’s result that the trace norm preserves positive semidefiniteness of 3 ×3 partitioned...
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Busch–Gudder metric on the Cone of Positive Semidefinite Operators and Its Isometries
In this paper we introduce a new distance measure called Busch–Gudder metric on the cone of all positive semidefinite operators acting on a complex...
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On Poles of the Resolvents of Dominated Elements in Ordered Banach Algebras
Let x and y be elements of an ordered Banach algebra (OBA) such that 0 ≤ x ≤ y. In this paper we will discuss results that give conditions under...
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On L-, M-Weakly Compact and Rank-One Operators
The finite rank, L- and M-weakly compact operators are studied. The inclusion of these classes with one another and with the weak Dunford–Pettis,...
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A Note on Universal Operators
An operator T is called universal for the complement of the ideal A if T does not belong to A, and factors through every element of the complement of...
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Operators that attain their minima
In this paper we study the theory of operators on complex Hilbert spaces, which attain theirminima in the unit sphere. We prove someimportant results...
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On Positivity and Roots in Operator Algebras
In earlier papers the second author and Charles Read have introduced and studied a new notion of positivity for operator algebras, with an eye to...
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On Means of Nonnegative Sesquilinear Forms
The aim of this paper is to generalize the theory of operator connections for nonnegative sesquilinear forms. As an application, we investigate the...
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Maximality of the Sum of a Maximally Monotone Linear Relation and a Maximally Monotone Operator
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided...
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A multivariate extension of an inequality of Brenner–Alzer
In this paper, we present a more general and extended form in a multivariate setting of an inequality of Brenner and Alzer.
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Parallel subtraction of nonnegative forms
The notions of parallel sum and parallel difference of two nonnegative forms were introduced and studied by Hassi, Sebestyén, and de Snoo in [13]...
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Some compactness properties of L-weakly and M-weakly compact operators
We present some compactness properties of L -weakly and M -weakly compact operators on a Banach lattice under additional conditions. Thus, we can say...