Positive definite hermitian mappings associated to tripotent elements
Antonio M. Peralta
TL;DR
This paper presents a straightforward proof of a significant result related to positive definite hermitian mappings in JB*-triples, simplifying the original proof by Friedman and Russo from 1985 using functional analysis techniques.
Contribution
The paper offers a simplified proof of a key theorem on hermitian mappings in JB*-triples, avoiding complex holomorphic methods used in prior work.
Findings
Simplified proof of Friedman and Russo's 1985 result
New proof relies solely on JB*-triple axioms and functional analysis
Enhances understanding of positive definite hermitian mappings
Abstract
We give a simple proof of a meaningful result established by Y. Friedman and B. Russo in 1985, whose proof was originally based on strong holomorphic results. We provide a simple proof which is directly deduced from the axioms of JB*-triples with techniques of Functional Analysis.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Geometric and Algebraic Topology · Holomorphic and Operator Theory