Geodesic
The single-valued extension property for sums and products of commuting operators
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 635-642 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 47A11, 47B40
Keywords: single-valued extension property; Dunford’s property $\mathrm (C)$; decomposable operators 
@article{CMJ_2002_52_3_a15,
     author = {Miller, T. L. and Neumann, M. M.},
     title = {The single-valued extension property for sums and products of commuting operators},
     journal = {Czechoslovak Mathematical Journal},
     pages = {635--642},
     year = {2002},
     volume = {52},
     number = {3},
     mrnumber = {1923267},
     zbl = {1075.47500},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a15/}
}
TY  - JOUR
AU  - Miller, T. L.
AU  - Neumann, M. M.
TI  - The single-valued extension property for sums and products of commuting operators
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 635
EP  - 642
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a15/
LA  - en
ID  - CMJ_2002_52_3_a15
ER  - 
%0 Journal Article
%A Miller, T. L.
%A Neumann, M. M.
%T The single-valued extension property for sums and products of commuting operators
%J Czechoslovak Mathematical Journal
%D 2002
%P 635-642
%V 52
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a15/
%G en
%F CMJ_2002_52_3_a15
Miller, T. L.; Neumann, M. M. The single-valued extension property for sums and products of commuting operators. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 635-642. http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a15/

[1] E. Albrecht and J.  Eschmeier: Analytic functional models and local spectral theory. Proc. London Math. Soc. 75 (1997), 323–348. | MR

[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

[3] C. Apostol: Decomposable multiplication operators. Rev. Roumaine Math. Pures Appl. 17 (1972), 323–333. | MR | Zbl

[4] B. Aupetit and D.  Drissi: Local spectrum and subharmonicity. In: Proc. Edinburgh Math. Soc. Vol. 39, 1996, pp. 571–579. | MR

[5] I. Colojoară and C.  Foiaş: Theory of Generalized Spectral Operators. Gordon and Breach, New York, 1968. | MR

[6] J. Eschmeier: Spectral decompositions and decomposable multipliers. Manuscripta Math. 51 (1985), 201–224. | DOI | MR | Zbl

[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

[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

[9] R. Lange and S. Wang: New Approaches in Spectral Decomposition. Contemp. Math. 128. Amer. Math. Soc., Providence, RI, 1992. | MR

[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

[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. | DOI | MR

[12] M. M. Neumann: On local spectral properties of operators on Banach spaces. Rend. Circ. Mat. Palermo (2), Suppl. 56 (1998), 15–25. | MR | Zbl

[13] S. L. Sun: The sum and product of decomposable operators. Northeast. Math.  J. 5 (1989), 105–117. (Chinese) | MR | Zbl

[14] F.-H. Vasilescu: Analytic Functional Calculus and Spectral Decompositions. Editura Academiei and D.  Reidel Publ. Company, Bucharest and Dordrecht, 1982. | MR | Zbl

[15] P. Vrbová: On local spectral properties of operators in Banach spaces. Czechoslovak Math. J. 23(98) (1973), 483–492. | MR