Approximate isometries of Hilbert spaces
Peter Semrl
TL;DR
This paper enhances the understanding of approximate isometries in real Hilbert spaces by removing the need for surjectivity, thus broadening the applicability of stability results.
Contribution
It provides an improved stability theorem for isometries of real Hilbert spaces without requiring surjectivity, advancing the theoretical framework.
Findings
Removed the surjectivity assumption in stability results
Established new bounds for approximate isometries
Extended the applicability of Hyers-Ulam stability
Abstract
We improve the Hyers-Ulam stability result for isometries of real Hilbert spaces by removing the surjectivity assumption.
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Taxonomy
TopicsAdvanced Banach Space Theory · Optimization and Variational Analysis · Fixed Point Theorems Analysis