On the defect spectrum of an extension of a Banach space operator

Vladimír Kordula

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 4, page 609-616
  • ISSN: 0011-4642

Abstract

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Let T be an operator acting on a Banach space X . We show that between extensions of T to some Banach space Y X which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.

How to cite

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Kordula, Vladimír. "On the defect spectrum of an extension of a Banach space operator." Czechoslovak Mathematical Journal 48.4 (1998): 609-616. <http://eudml.org/doc/30441>.

@article{Kordula1998,
abstract = {Let $T$ be an operator acting on a Banach space $X$. We show that between extensions of $T$ to some Banach space $Y\supset X$ which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.},
author = {Kordula, Vladimír},
journal = {Czechoslovak Mathematical Journal},
keywords = {extensions of operators; approximate point spectrum; defect spectrum},
language = {eng},
number = {4},
pages = {609-616},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the defect spectrum of an extension of a Banach space operator},
url = {http://eudml.org/doc/30441},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Kordula, Vladimír
TI - On the defect spectrum of an extension of a Banach space operator
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 4
SP - 609
EP - 616
AB - Let $T$ be an operator acting on a Banach space $X$. We show that between extensions of $T$ to some Banach space $Y\supset X$ which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.
LA - eng
KW - extensions of operators; approximate point spectrum; defect spectrum
UR - http://eudml.org/doc/30441
ER -

References

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  1. 10.4153/CJM-1982-031-1, Canad. J. Math. 34 (1982), 466–483. (1982) MR0658979DOI10.4153/CJM-1982-031-1
  2. To what extent can the spectrum of an operator be diminished under an extension, in: Linear and Complex Analysis Problem Book, V. P. Havin, S. V. Hruščev and N. K. Nikol’skij (eds.), Lecture Notes in Math. 1043, Springer, Berlin 1984, 210, . 
  3. Adjoint inverses to noncommutative Banach algebras and extensions of operator, Studia Math. 91 (1988), 73–77. (1988) MR0957286
  4. On the joint essential spectrum of commuting operators, Acta Sci. Math. Szeged 57 (1993), 199–205. (1993) MR1243277
  5. 10.1090/S0002-9947-1988-0946450-5, Trans. Amer. Math. Soc. 308 (1988), 413–429. (1988) MR0946450DOI10.1090/S0002-9947-1988-0946450-5
  6. On the joint spectra of commuting families of operators, Studia Math. 50 (1974), 127–148. (1974) MR0346555
  7. On a problem concerning joint approximate point spectra, Studia Math. 45 (1973), 239–240. (1973) Zbl0256.47002MR0336382

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