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Weyl spectrum of the products of operators

Xiaohong Cao
대한수학회 (The Korean Mathematical Society)|2008.05|대한수학회지 (Journal of the KMS)|제45권 제3호|pp. 771-780

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참고문헌

키워드

Weyl spectrumWeyl’s theoremBrowder’s theoremessential approximate point spectrum.
주제분류수학

초록

Let MC = (수식) be a 2×2 upper triangular operator matrix acting on the Hilbert space H K and let σw(ㆍ) denote theWeyl spectrum. We give the necessary and sufficient conditions for operators A and B which [수식] holds for every C ∈ B(K, H). We also study the Weyl’s theorem for operator matrices.

Abstract

Let MC = (수식) be a 2×2 upper triangular operator matrix acting on the Hilbert space H K and let σw(ㆍ) denote theWeyl spectrum. We give the necessary and sufficient conditions for operators A and B which [수식] holds for every C ∈ B(K, H). We also study the Weyl’s theorem for operator matrices.

참고문헌 (20)

  1. R. Bouldin, "The product of operators with closed range", Tohoku Mathematical Journal, 25, pp.359~363 (1973)
  2. X. H. Cao, "Essential approximate point spectra and Weyl’s theorem for operator matrices", Journal of Mathematical Analysis and Applications, 304(2), pp.759~771 (2005)
  3. Bhagwati P. Duggal, "On Weyl's theorem for quasi-class $A$ operators", 대한수학회보, 43(4), pp.899~909 (2006), 대한수학회
  4. Bhagwati Prashad Duggal, "WEYL'S THEOREMS FOR POSINORMAL OPERATORS", 대한수학회보, 42(3), pp.529~541 (2005), 대한수학회
  5. I. Gohberg, "Classes of linear operators. Vol. I, Operator Theory: Advances and Applications", pp.49~ (1990), Birkhauser Verlag
  6. S. Grabiner, "Uniform ascent and descent of bounded operators", Journal of the Mathematical Society of Japan, 34(2), pp.317~337 (1982)
  7. R. Harte, "Another note on Weyl’s theorem", Transactions of the American Mathematical Society, 349(5), pp.2115~2124 (1997)
  8. W. Y. Lee, "Weyl’s theorem for operator matrices", Integral Equations Operator Theory, 32(3), pp.319~331 (1998)
  9. W. Y. Lee, "Weyl spectra of operator matrices", Proc. Amer. Math. Soc., 통권 : 129, pp.131~138 (2001)
  10. H. Weyl, "Uber beschrankte quadratische Formen, deren Differenz vollsteig ist", Rendiconti del Circolo Matematico di Palermo, 27, pp.373~392 (1909)
  11. R. Bouldin, "The product of operators with closed range", Tohoku Mathematical Journal, 25(2), pp.359~363 (1973)
  12. X. H. Cao, "Essential approximate point spectra and Weyl’s theorem for operator matrices", Journal of Mathematical Analysis and Applications, 304(2), pp.759~771 (2005)
  13. Bhagwati P. Duggal, "On Weyl's theorem for quasi-class $A$ operators", 대한수학회보, 43(4), pp.899~909 (2006), 대한수학회
  14. Bhagwati Prashad Duggal, "WEYL'S THEOREMS FOR POSINORMAL OPERATORS", 대한수학회보, 42(3), pp.529~541 (2005), 대한수학회
  15. I. Gohberg, "Classes of linear operators. Vol. I, Operator Theory: Advances and Applications", pp.49~ (1990), Birkhauser Verlag
  16. S. Grabiner, "Uniform ascent and descent of bounded operators", Journal of the Mathematical Society of Japan, 34(2), pp.317~337 (1982)
  17. R. Harte, "Another note on Weyl’s theorem", Transactions of the American Mathematical Society, 349(5), pp.2115~2124 (1997)
  18. W. Y. Lee, "Weyl’s theorem for operator matrices", Integral Equations Operator Theory, 32(3), pp.319~331 (1998)
  19. W. Y. Lee, "Weyl spectra of operator matrices", Proc. Amer. Math. Soc., 통권 : 129, pp.131~138 (2001)
  20. H. Weyl, "Uber beschrankte quadratische Formen, deren Differenz vollsteig ist", Rendiconti del Circolo Matematico di Palermo, 27, pp.373~392 (1909)

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