Alternatingly Hyperexpansive Operator Tuples

Alternatingly Hyperexpansive Operator Tuples The notion of an alternatingly hyperexpansive operator on a Hilbert space is generalized to that of an alternatingly hyperexpansive operator tuple, which necessitates exploring the theory of absolutely monotone functions as defined on the m-fold product N m of the semi-group N of non-negative integers and as defined on semi-open cubes in the m-dimensional real Euclidean space R m. The multi-variable Laplace transform and the Stieltjes Moment Problem make a natural appearance in the development of the relevant theory, which also highlights the close connections of alternatingly hyperexpansive operator tuples with completely hyperexpansive and subnormal ones. In particular, if T is subnormal and the joint (Taylor) spectrum of its minimal normal extension is contained in a certain subset of the Hermitian space C m, then T turns out to be alternatingly hyperexpansive. In the context of multi-variable weighted shifts, the last assertion can be related to the notion of a Stieltjes Moment Net. The general characterization of an alternatingly hyperexpansive m-variable weighted shift T, however, requires a certain net of (positive) numbers associated with T to be absolutely monotone on N m and allows for such a T to be non-subnormal. Positivity Springer Journals

Alternatingly Hyperexpansive Operator Tuples

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Kluwer Academic Publishers
Copyright © 2001 by Kluwer Academic Publishers
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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  • On completely hyperexpansive operators
    Athavale, A.
  • Completely hyperexpansive operator tuples
    Athavale, A.; Sholapurkar, V.M.

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