A Note on the Norm and Spectrum of a Foguel Operator
Mrinal Raghupathi
TL;DR
This paper introduces two methods for computing the norm of a Foguel operator, providing simpler proofs and extending existing results in operator theory.
Contribution
It offers algebraic and Schur complement-based techniques for Foguel operator norm calculation, simplifying previous proofs and extending theoretical understanding.
Findings
Two methods for computing Foguel operator norms are presented.
Simplified proofs of existing results are provided.
Extensions of the norm computation techniques are discussed.
Abstract
We present two ways to compute the norm of a Foguel operator. One of these is algebraic and the other makes use of the Schur complement. This gives a two simpler proof of a result of Garcia. We also provide an extension of these results.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Matrix Theory and Algorithms