Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Equivalent conditions for decomposable operators


Author: Ridgley Lange
Journal: Proc. Amer. Math. Soc. 82 (1981), 401-406
MSC: Primary 47B40
DOI: https://doi.org/10.1090/S0002-9939-1981-0612729-9
MathSciNet review: 612729
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Several new characterizations of an arbitrary decomposable operator on Banach space are given; for example, one of these is in terms of spectral conditions on an arbitrary invariant subspace, while another uses the spectral manifold $ {X_T}({G^ - })$ (rather than $ {X_T}(F)$). From these results a short proof of Frunza's duality theorem is derived. Finally we give sufficient conditions that the predual of a decomposable operator is of the same class.


References [Enhancements On Off] (What's this?)

  • [1] C. Apostol, Roots of decomposable operator-valued functions, Rev. Roumaine Math. Pures Appl. 13 (1968), 433-438. MR 0233225 (38:1548)
  • [2] I. Erdélyi and R. Lange, Operators with spectral decomposition properties, J. Math. Anal. Appl. 66 (1978), 1-19. MR 513482 (80d:47058)
  • [3] J. Finch, The single-valued extension property in Banach spaces, Pacific J. Math. 48 (1975), 61-69. MR 0374985 (51:11181)
  • [4] C. Foiaş, Spectral maximal spaces and decomposable operators, Arch. Math. (Basel) 14 (1963), 341-349. MR 0152893 (27:2865)
  • [5] ş. Frunza, A duality theorem for decomposable operators, Rev. Roumaine Math. Pures Appl. 16 (1971), 1055-1058. MR 0301552 (46:710)
  • [6] A. Jafarian and F.-H. Vasilescu, A characterization of $ 2$-decomposable operators, Rev. Roumaine Math. Pures Appl. 19 (1974), 769-771. MR 0358423 (50:10889)
  • [7] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Heidelberg, 1966. MR 0203473 (34:3324)
  • [8] R. Lange, Analytically decomposable operators, Trans. Amer. Math. Soc. 244 (1978), 225-240. MR 506617 (80e:47032)
  • [9] M. Radjabalipour, On equivalence of decomposable and $ 2$-decomposable operators, Pacific J. Math. 28 (1978), 243-247. MR 507632 (80c:47032)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B40

Retrieve articles in all journals with MSC: 47B40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0612729-9
Keywords: Decomposable operator, spectral maximal space
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society