On the norm of linear combinations of projections and some characterizations of Hilbert spaces

Nahum Krupnik, Alexander Markus

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Let B be a Banach space and let P,Q (P,Q ≠ 0) be two complementary projections in B (i.e., P + Q = I). For dimB > 2 we show that formulas of the kind ||aP + bQ|| = f(a, b, ||P||) hold if and only if the norm in B can be induced by an inner product. The two-dimensional case needs special consideration which is done in the last two sections.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Pages501-510
Number of pages10
DOIs
StatePublished - 2017

Publication series

NameOperator Theory: Advances and Applications
Volume259
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Bibliographical note

Publisher Copyright:
© 2017 Springer International Publishing.

Keywords

  • Characterizations of Hilbert spaces
  • Linear combinations of two additional projections
  • Projections

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