A generalization of Vesentini and Wermer's theorems

Zbigniew Slodkowski

Rendiconti del Seminario Matematico della Università di Padova (1986)

  • Volume: 75, page 157-171
  • ISSN: 0041-8994

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Slodkowski, Zbigniew. "A generalization of Vesentini and Wermer's theorems." Rendiconti del Seminario Matematico della Università di Padova 75 (1986): 157-171. <http://eudml.org/doc/108017>.

@article{Slodkowski1986,
author = {Slodkowski, Zbigniew},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {preanalytic family; invertible operators; analytic operator-valued functions; topological embeddings; invariant subspace; subharmonic function; subanalytic family of complex Banach spaces; analytic family of bounded operators with locally uniformly bounded norm; quasi-subharmonic; set-valued function},
language = {eng},
pages = {157-171},
publisher = {Seminario Matematico of the University of Padua},
title = {A generalization of Vesentini and Wermer's theorems},
url = {http://eudml.org/doc/108017},
volume = {75},
year = {1986},
}

TY - JOUR
AU - Slodkowski, Zbigniew
TI - A generalization of Vesentini and Wermer's theorems
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1986
PB - Seminario Matematico of the University of Padua
VL - 75
SP - 157
EP - 171
LA - eng
KW - preanalytic family; invertible operators; analytic operator-valued functions; topological embeddings; invariant subspace; subharmonic function; subanalytic family of complex Banach spaces; analytic family of bounded operators with locally uniformly bounded norm; quasi-subharmonic; set-valued function
UR - http://eudml.org/doc/108017
ER -

References

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  1. [1] B. AupetitAnalytic multivalued functions in Banach algebras and uniform algebras, Advances in Mathematics, 44 (1982), pp. 18-60. Zbl0486.46041MR654547
  2. [2] B. Aupetit - J. WERMER, Capacity and uniform algebras, J. Functional Analysis, 28 (1978), pp. 386-400. Zbl0378.46045MR496966
  3. [3] J. Leiterer, Banach coherent analytic Frechet sheaves, Math. Nachr., 85 (1978), pp. 91-109. Zbl0409.32017MR517643
  4. [4] K. Oka, Note sur les familles de fonctions analytiques multiformes, etc., J. Sci. Hiroshima Univ., Ser. A, 4 (1934), pp. 93-98. Zbl0011.31403
  5. [5] T.J. Ransford, Analytic multivalued functions, Thesis for Smith Competition, University of Cambridge (1983). 
  6. [6] R. Rochberg et al., A theory of complex interpolation for families of Banach spaces, Advances in Mathematics, 43 (1982), pp. 203-229. Zbl0501.46065MR648799
  7. [7] Z. Slodkowski, On subharmonicity of the capacity of the spectrum, Proc. Amer. Math. Soc., 81 (1981), pp. 243-249. Zbl0407.46046MR593466
  8. [8] Z. Slodkowski, Analytic set-valued functions and spectra, Math. Ann., 256 (1981), pp. 363-386. Zbl0452.46028MR626955
  9. [8a] Z. Slodkowski, Analytic set-valued functions and spectra, Preprint series of the Institute of Mathematics of the Polish Academy of Sciences (1980). Zbl0471.46034MR626955
  10. [9] Z. Slodkowski, Operators with closed ranges in spaces of analytic vector-valued functions, J. Functional Analysis (to appear). Zbl0611.46046MR865219
  11. [10] M.A. Shubin, On holomorphic families of subspaces of a Banach space, Matem. Issled. Kishinev, 5 (1970), pp. 153-165. Zbl0233.32024MR285730
  12. [11] E. Vesentini, On the subharmonicity of the spectral radius, Boll. Un. Mat. Ital., 4 (1968), pp. 427-429. MR244766
  13. [12] J. Wermer, Subharmonicity and hulls, Pacific J. Math., 58 (1975), pp. 283-290. Zbl0308.32011MR393567

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