The norm and modulus of a Foguel operator
Stephan Ramon Garcia
TL;DR
This paper introduces a method to compute the norm and spectrum of Foguel operators, providing exact calculations or bounds, and explores their intriguing links to the Golden Ratio.
Contribution
The paper presents a novel approach for analyzing Foguel operators' norms and spectra, including exact formulas and bounds, and uncovers connections to the Golden Ratio.
Findings
Exact norm calculations for many Foguel operators
Sharp upper bounds for the norm in complex cases
Connections between Foguel operators and the Golden Ratio
Abstract
We develop a method for calculating the norm and the spectrum of the modulus of a Foguel operator. In many cases, the norm can be computed exactly. In others, sharp upper bounds are obtained. In particular, we observe several connections between Foguel operators and the Golden Ratio.
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