TL;DR
This paper clarifies misconceptions about the spectra of partial operators, emphasizing that void or unbounded spectra are not solely due to unboundedness, contrary to traditional beliefs.
Contribution
It challenges and corrects the common understanding of spectral properties of partial operators as presented in classical literature.
Findings
Partial operators can have void spectra without being unbounded.
Unboundedness is not the sole reason for void or unbounded spectra.
The paper provides a revised perspective on spectral theory for partial operators.
Abstract
Partial operators can have void or unbounded spectra. Contrarily to what is written in Dunford-Schwarz, the reason is not in the fact they are unounded operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Operator Algebra Research · Advanced Banach Space Theory