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Additive combinations of special operators

Pei Wu (1994)

Banach Center Publications

This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible operators...

Analytic formulas for the hyperbolic distance between two contractions

Ion Suciu (1997)

Annales Polonici Mathematici

In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values...

Antieigenvalue analysis for continuum mechanics, economics, and number theory

Karl Gustafson (2016)

Special Matrices

My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

I. Gil’, Michael (2009)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 47A56, 47A57,47A63We derive bounds for the norms of the fractional powers of operators with compact Hermitian components, and operators having compact inverses in a separable Hilbert space. Moreover, for these operators, as well as for dissipative operators, the constants in the moment inequalities are established.* This research was supported by the Kamea Fund of Israel.

Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields

Yves Colin de Verdière, Nabila Torki-Hamza, Françoise Truc (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We define the magnetic Schrödinger operator on an infinite graph by the data of a magnetic field, some weights on vertices and some weights on edges. We discuss essential self-adjointness of this operator for graphs of bounded degree. The main result is a discrete version of a result of two authors of the present paper.

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