Full operators and algebras generated by invertible operators
Wilson R. Pacheco R
TL;DR
This paper characterizes full operators and explores properties of nonfull injective operators, also addressing when inverses can be approximated by polynomials in the operator.
Contribution
It provides a characterization of full operators and answers open questions about polynomial approximation of inverses in operator theory.
Findings
Full operators are characterized with specific properties.
Nonfull injective operators exhibit distinct properties.
Conditions are identified under which inverses can be weakly approximated by polynomials.
Abstract
In the present work we characterized full operators and we showed some properties that have nonfull injectives operators. With the results developed for full operators, we affirmatively respond two questions formulated by Bravo and Feintuch on when the inverse of an operator can be weakly approximated by polynomials in the operator
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Matrix Theory and Algorithms · Advanced Algebra and Logic