A spectrality condition for infinitesimal generators of cosine operator functions

Authors

  • Amina Šahović University ``Džemal Bijedić'', USRC ``M. Hujdur-Hujka'', 88000 Mostar, Bosnia and Herzegovina Author
  • Fikret Vajzović Faculty of Natural Sciences and Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71000 Sarajevo, Bosnia and Herzegovina Author

Keywords:

Cosine operator function, hermitian operator, strictly convex Banach space, G\^ateaux differentiable norm, spectral operator

Subjects:

47D09, 46C50, 47B40

Abstract

We will give a necessary and sufficient condition for the infinitesimal generator of a stronglycontinuous cosine operator function $C(t)$, such that $\|C(t)\|\le1$ for all $tın R$ on a reflexive, strictly convex(complex) Banach space with a G\^ateaux differentiable norm to be a spectral scalar type operator with the spectralfamily of hermitian bounded linear projectors.

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Published

2008-07-15

Issue

Vol. 60 No. 3 (2008): Vol. 60, Issue 3

Section

Articles

License

Copyright (c) 2008 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.