Title:
|
The single-valued extension property for sums and products of commuting operators (English) |
Author:
|
Miller, T. L. |
Author:
|
Neumann, M. M. |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
52 |
Issue:
|
3 |
Year:
|
2002 |
Pages:
|
635-642 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
It is shown that the sum and the product of two commuting Banach space operators with Dunford’s property $\mathrm (C)$ have the single-valued extension property. (English) |
Keyword:
|
single-valued extension property |
Keyword:
|
Dunford’s property $\mathrm (C)$ |
Keyword:
|
decomposable operators |
MSC:
|
47A11 |
MSC:
|
47B40 |
idZBL:
|
Zbl 1075.47500 |
idMR:
|
MR1923267 |
. |
Date available:
|
2009-09-24T10:54:56Z |
Last updated:
|
2020-07-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127749 |
. |
Reference:
|
[1] E. Albrecht and J. Eschmeier: Analytic functional models and local spectral theory.Proc. London Math. Soc. 75 (1997), 323–348. MR 1455859 |
Reference:
|
[2] E. Albrecht, J. Eschmeier and M. M. Neumann: Some topics in the theory of decomposable operators.In: Advances in Invariant Subspaces and Other Results of Operator Theory. Operator Theory: Advances and Applications, Vol. 17, Birkhäuser Verlag, Basel, 1986, pp. 15–34. MR 0901056 |
Reference:
|
[3] C. Apostol: Decomposable multiplication operators.Rev. Roumaine Math. Pures Appl. 17 (1972), 323–333. Zbl 0239.47013, MR 0310665 |
Reference:
|
[4] B. Aupetit and D. Drissi: Local spectrum and subharmonicity.In: Proc. Edinburgh Math. Soc. Vol. 39, 1996, pp. 571–579. MR 1417698 |
Reference:
|
[5] I. Colojoară and C. Foiaş: Theory of Generalized Spectral Operators.Gordon and Breach, New York, 1968. MR 0394282 |
Reference:
|
[6] J. Eschmeier: Spectral decompositions and decomposable multipliers.Manuscripta Math. 51 (1985), 201–224. Zbl 0578.47024, MR 0788679, 10.1007/BF01168353 |
Reference:
|
[7] J. Eschmeier, K. B. Laursen and M. M. Neumann: Multipliers with natural local spectra on commutative Banach algebras.J. Funct. Analysis 138 (1996), 273–294. MR 1395959 |
Reference:
|
[8] R. Kantrowitz and M. M. Neumann: On certain Banach algebras of vector-valued functions.In: Function spaces, the second conference. Lecture Notes in Pure and Applied Math. Vol. 172, Marcel Dekker, New York, 1995, pp. 223–242. MR 1352233 |
Reference:
|
[9] R. Lange and S. Wang: New Approaches in Spectral Decomposition. Contemp. Math. 128.Amer. Math. Soc., Providence, RI, 1992. MR 1162741 |
Reference:
|
[10] K. B. Laursen and M. M. Neumann: Asymptotic intertwining and spectral inclusions on Banach spaces.Czechoslovak Math. J. 43(118) (1993), 483–497. MR 1249616 |
Reference:
|
[11] T. L. Miller and V. G. Miller: An operator satisfying Dunford’s condition $\mathrm (C)$ but without Bishop’s property $(\text{b})$.Glasgow Math. J. 40 (1998), 427–430. MR 1660054, 10.1017/S0017089500032754 |
Reference:
|
[12] M. M. Neumann: On local spectral properties of operators on Banach spaces.Rend. Circ. Mat. Palermo (2), Suppl. 56 (1998), 15–25. Zbl 0929.47001, MR 1710819 |
Reference:
|
[13] S. L. Sun: The sum and product of decomposable operators.Northeast. Math. J. 5 (1989), 105–117. (Chinese) Zbl 0699.47022, MR 1010749 |
Reference:
|
[14] F.-H. Vasilescu: Analytic Functional Calculus and Spectral Decompositions.Editura Academiei and D. Reidel Publ. Company, Bucharest and Dordrecht, 1982. Zbl 0495.47013, MR 0690957 |
Reference:
|
[15] P. Vrbová: On local spectral properties of operators in Banach spaces.Czechoslovak Math. J. 23(98) (1973), 483–492. MR 0322536 |
. |