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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  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. 10.4064/sm-91-1-73-77, Studia Math. 91 (1988), 73–77. (1988) MR0957286DOI10.4064/sm-91-1-73-77
  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. 10.4064/sm-50-2-127-148, Studia Math. 50 (1974), 127–148. (1974) MR0346555DOI10.4064/sm-50-2-127-148
  7. 10.4064/sm-45-3-239-240, Studia Math. 45 (1973), 239–240. (1973) Zbl0256.47002MR0336382DOI10.4064/sm-45-3-239-240

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