PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 134 | 2 | 111-117
Tytuł artykułu

Perturbation theorems for Hermitian elements in Banach algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
Słowa kluczowe
Twórcy
autor
Bibliografia
  • [1] B. Aupetit, A Primer on Spectral Theory, Springer, 1991.
  • [2] B. Aupetit and D. Drissi Local spectrum and subharmonicity, Proc. Edinburgh Math. Soc. 39 (1996), 571-579.
  • [3] R. Bhatia, Matrix Analysis, Springer, 1997.
  • [4] R. Bhatia, C. Davis and P. Koosis, An extremal problem in Fourier analysis with applications to operator theory, J. Funct. Anal. 82 (1989), 138-150.
  • [5] R. Bhatia, C. Davis and A. McIntosh, Perturbation of spectral subspaces and solution of linear operator equations, Linear Algebra Appl. 52-53 (1983), 45-67.
  • [6] R. Bhatia and P. Rosenthal, How and why to solve the operator equation AX - XB = Y, Bull. London Math. Soc. 29 (1997), 1-21.
  • [7] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, Cambridge Univ. Press, 1971.
  • [8] A. Browder, On Bernstein's inequality and the norm of Hermitian operators, Amer. Math. Monthly 78 (1971), 871-873.
  • [9] D. E. Evans, On the spectrum of a one-parameter strongly continuous representation, Math. Scand. 39 (1976), 80-82.
  • [10] U. Haagerup and L. Zsidó, Resolvent estimate for Hermitian operators and a related minimal extrapolation problem, Acta Sci. Math. (Szeged) 59 (1994), 503-524.
  • [11] V. E. Katsnelson, A conservative operator has norm equal to its spectral radius, Mat. Issled. 5 (1970), 186-189 (in Russian).
  • [12] A. N. Kolmogorov, On inequalities between upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Uchen. Zap. Moskov. Gos. Univ. Mat. 30 (1939), 3-16 (in Russian); English transl.: Amer. Math. Soc. Transl. 4 (1949), 233-243.
  • [13] B. Ya. Levin, Lectures on Entire Functions, Transl. Math. Monographs 150, Amer. Math. Soc., 1996.
  • [14] R. McEachin, A sharp estimate in an operator inequality, Proc. Amer. Math. Soc. 115 (1992), 161-165.
  • [15] J. R. Partington, The resolvent of a Hermitian operator on a Banach space, J. London Math. Soc. (2) 27 (1983), 507-512.
  • [16] A. M. Sinclair, The norm of a Hermitian element in a Banach algebra, Proc. Amer. Math. Soc. 28 (1971), 446-450.
  • [17] B. Sz.-Nagy, Über die Ungleichung von H. Bohr, Math. Nachr. 9 (1953), 255-259.
  • [18] B. Sz.-Nagy and A. Strausz, On a theorem of H. Bohr, Mat. Termész. Értes. 57 (1938), 121-133 (in Hungarian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv134i2p111bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.