On the semi-Browder spectrum

Vladimír Kordula; Vladimír Müller; Vladimir Rakočević

Studia Mathematica (1997)

  • Volume: 123, Issue: 1, page 1-13
  • ISSN: 0039-3223

Abstract

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An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators.

How to cite

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Kordula, Vladimír, Müller, Vladimír, and Rakočević, Vladimir. "On the semi-Browder spectrum." Studia Mathematica 123.1 (1997): 1-13. <http://eudml.org/doc/216378>.

@article{Kordula1997,
abstract = {An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators.},
author = {Kordula, Vladimír, Müller, Vladimír, Rakočević, Vladimir},
journal = {Studia Mathematica},
keywords = {upper (lower) semi-Browder; upper (lower) semi-Fredholm; finite ascent (descent); -tuples of commuting operators; joint spectrum; (essentially) semiregular operators},
language = {eng},
number = {1},
pages = {1-13},
title = {On the semi-Browder spectrum},
url = {http://eudml.org/doc/216378},
volume = {123},
year = {1997},
}

TY - JOUR
AU - Kordula, Vladimír
AU - Müller, Vladimír
AU - Rakočević, Vladimir
TI - On the semi-Browder spectrum
JO - Studia Mathematica
PY - 1997
VL - 123
IS - 1
SP - 1
EP - 13
AB - An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators.
LA - eng
KW - upper (lower) semi-Browder; upper (lower) semi-Fredholm; finite ascent (descent); -tuples of commuting operators; joint spectrum; (essentially) semiregular operators
UR - http://eudml.org/doc/216378
ER -

References

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  1. [1] J. J. Buoni, R. Harte and T. Wickstead, Upper and lower Fredholm spectra, Proc. Amer. Math. Soc. 66 (1977), 309-314. Zbl0375.47001
  2. [2] S. R. Caradus, W. E. Pfaffenberger and B. Yood, Calkin Algebras and Algebras of Operators on Banach Spaces, Marcel Dekker, 1974. Zbl0299.46062
  3. [3] R. E. Curto and A. T. Dash, Browder spectral systems, Proc. Amer. Math. Soc. 103 (1988), 407-413. Zbl0662.47003
  4. [4] S. Grabiner, Ascent, descent, and compact perturbations, ibid. 71 (1978), 79-80. 
  5. [5] S. Grabiner, Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317-337. Zbl0477.47013
  6. [6] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, 1988. Zbl0636.47001
  7. [7] R. E. Harte and A. W. Wickstead, Upper and lower Fredholm spectra II, Math. Z. 154 (1977), 253-256. Zbl0393.47001
  8. [8] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261-322. Zbl0090.09003
  9. [9] V. Kordula, The essential Apostol spectrum and finite dimensional perturbations, Proc. Roy. Irish Acad., to appear. Zbl0880.47005
  10. [10] V. Kordula and V. Müller, The distance from the Apostol spectrum, Proc. Amer. Math. Soc., to appear. Zbl0861.47008
  11. [11] V. Kordula and V. Müller, On the axiomatic theory of spectrum, Studia Math. 119 (1996), 109-128. Zbl0857.47001
  12. [12] H. Kroh and P. Volkmann, Störungssätze für Semifredholmoperatoren, Math. Z. 148 (1976), 295-297. Zbl0318.47008
  13. [13] M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105. Zbl0694.47002
  14. [14] M. Mbekhta and V. Müller, On the axiomatic theory of spectrum II, Studia Math. 119 (1996), 129-147. Zbl0857.47002
  15. [15] M. Mbekhta et A. Ouahab, Contribution à la théorie spectrale généralisé dans les espaces de Banach, C. R. Acad. Sci. Paris 313 (1991), 833-836. Zbl0742.47001
  16. [16] V. Müller, On the regular spectrum, J. Operator Theory 31 (1994), 363-380. Zbl0845.47005
  17. [17] M. Putinar, Functional calculus and the Gelfand transformation, Studia Math. 84 (1984), 83-86. Zbl0498.47009
  18. [18] V. Rakočević, Approximate point spectrum and commuting compact perturbations, Glasgow Math. J. 28 (1986), 193-198. Zbl0602.47003
  19. [19] V. Rakočević, Generalized spectrum and commuting compact perturbations, Proc. Edinburgh Math. Soc. 36 (1993), 197-209. Zbl0794.47003
  20. [20] V. Rakočević, Semi-Fredholm operators with finite ascent or descent and perturbations, Proc. Amer. Math. Soc. 123 (1995), 3823-3825. Zbl0854.47008
  21. [21] V. Rakočević, Semi-Browder operators and perturbations, Studia Math. 122 (1996), 131-137. Zbl0892.47015
  22. [22] V. Rakočević, Semi-Fredholm operators with finite ascent or descent and corresponding spectra, in: Proc. Conf. in Priština, University of Priština, 1994, 79-89. Zbl0930.47006
  23. [23] C. Schmoeger, Ein Spektralabbildungssatz, Arch. Math. (Basel) 55 (1990), 484-489. Zbl0721.47005
  24. [24] T. T. West, A Riesz-Schauder theorem for semi-Fredholm operators, Proc. Roy. Irish Acad. 87 (1987), 137-146. Zbl0621.47016
  25. [25] W. Żelazko, Axiomatic approach to joint spectra I, Studia Math. 64 (1979), 249-261. Zbl0426.47002

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