VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • The group of isometries and the structure of a finite-dimensional Banach space
    Vidav, Ivan
    Let ▫$X$▫ be a finite-dimensional complex Banach space. The set ▫$G$▫ of all isometries on ▫$X$▫ is a compact Lie group. Let ▫$G_0$▫ be the identity component of ▫$G$▫. Further, denote by ▫${\cal ... K}(X)$▫ the set of all Hermitian operators on ▫$X$▫. It is shown that the space ▫${\cal K}(X)+i{\cal K}(X)$▫ is an algebra if and only if there exists a system of ▫$r$▫ orthogonal non-zero Hermitian idempotents on ▫$X$▫, where ▫$r={\rm ran}kG_0$▫. An easy consequence of this theorem is a result of H. Schneider and R.E.L. Turner on matrices Hermitian for an absolute norm.
    Vir: Publications of the Department of Mathematics. - ISSN 0459-6463 (Letn. 12, št. 83, 1977, str. 17-26)
    Vrsta gradiva - članek, sestavni del
    Leto - 1977
    Jezik - angleški
    COBISS.SI-ID - 7037785

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