THE CLASSICAL VOLTERRA OPERATOR AND SCHUR’S THEOREM
Source of Publication
Scientiae Mathematicae Japonicae
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].
Physical Sciences and Mathematics
Rodriguez-Martinez, Alejandro, "THE CLASSICAL VOLTERRA OPERATOR AND SCHUR’S THEOREM" (2009). All Works. 3363.
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