Spectral decomposition with monotonic spectral resolvents
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- by I. Erdélyi and Sheng Wang Wang PDF
- Trans. Amer. Math. Soc. 277 (1983), 851-859 Request permission
Abstract:
The spectral decomposition problem of a Banach space over the complex field entails two kinds of constructive elements: (1) the open sets of the field and (2) the invariant subspaces (under a given linear operator) of the Banach space. The correlation between these two structures, in the framework of a spectral decomposition, is the spectral resolvent concept. Special properties of the spectral resolvent determine special types of spectral decompositions. In this paper, we obtain conditions for a spectral resolvent to have various monotonic properties.References
- I. Erdélyi, Spectral resolvents, Operator theory and functional analysis (Papers, Summer Meeting, Amer. Math. Soc., Providence, R.I., 1978) Res. Notes in Math., vol. 38, Pitman, Boston, Mass.-London, 1979, pp. 51–70. MR 579021
- I. Erdélyi, Monotonic properties of some spectral resolvents, Libertas Math. 1 (1981), 117–124. MR 623367
- James K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), no. 1, 61–69. MR 374985, DOI 10.2140/pjm.1975.58.61
- Ciprian Foiaş, Spectral maximal spaces and decomposable operators in Banach space, Arch. Math. (Basel) 14 (1963), 341–349. MR 152893, DOI 10.1007/BF01234965
- Şt. Frunză, The single-valued extension property for coinduced operators, Rev. Roumaine Math. Pures Appl. 18 (1973), 1061–1065. MR 324445
- R. Lange, Strongly analytic subspaces, Operator theory and functional analysis (Papers, Summer Meeting, Amer. Math. Soc., Providence, R.I., 1978) Res. Notes in Math., vol. 38, Pitman, Boston, Mass.-London, 1979, pp. 16–30. MR 579018
- Mehdi Radjabalipour, Equivalence of decomposable and $2$-decomposable operators, Pacific J. Math. 77 (1978), no. 1, 243–247. MR 507632, DOI 10.2140/pjm.1978.77.243
- G. W. Shulberg, Spectral resolvents and decomposable operators, Operator theory and functional analysis (Papers, Summer Meeting, Amer. Math. Soc., Providence, R.I., 1978) Res. Notes in Math., vol. 38, Pitman, Boston, Mass.-London, 1979, pp. 71–84. MR 579022
- F.-H. Vasilescu, Residually decomposable operators in Banach spaces, Tohoku Math. J. (2) 21 (1969), 509–522. MR 275208, DOI 10.2748/tmj/1178242896
- F.-H. Vasilescu, On the residual decomposability in dual spaces, Rev. Roumaine Math. Pures Appl. 16 (1971), 1573–1587. MR 306965
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 277 (1983), 851-859
- MSC: Primary 47A10; Secondary 47A15
- DOI: https://doi.org/10.1090/S0002-9947-1983-0694393-2
- MathSciNet review: 694393