Title

THE CLASSICAL VOLTERRA OPERATOR AND SCHUR’S THEOREM

Author First name, Last name, Institution

Alejandro Rodriguez-Martinez, Zayed University

Document Type

Article

Source of Publication

Scientiae Mathematicae Japonicae

Publication Date

1-1-2009

Abstract

In this work we provide a counterexample for Schur’s Theorem on triangularmatrices on infinite dimensional spaces. Moreover, the counterexample provided is acompact quasinilpotent operator. Indeed, the result neither depends on the index ofthe chosen basis for the matrix representations nor on the upper-lower choice for thetriangular matrix. As a consequence, we see the optimality of a result by Halmos onmatrix representations of operators. Namely, Halmos proved that each operator canbe represented by a matrix with finite columns. Finally, we ‘answer’ a philosophicalquestion posed by J. B. Conway in [1, p.213].

Volume

70

Disciplines

Physical Sciences and Mathematics

Indexed in Scopus

no

Open Access

no

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