Browder spectral systems
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- by Raúl E. Curto and A. T. Dash PDF
- Proc. Amer. Math. Soc. 103 (1988), 407-413 Request permission
Abstract:
For two spectral systems ${\sigma _1}$ and ${\sigma _2}$ on a Banach space $\mathcal {X}$, the associated Browder spectral system is ${\sigma _{b;1,2}}: = {\sigma _1} \cup {\sigma ’_2}$. We prove that ${\sigma _{b;1,2}}$ possesses the projection and spectral mapping properties whenever ${\sigma _1}$ and ${\sigma _2}$ do (and satisfy a few additional mild assumptions). We also calculate ${\sigma _{b;1,2}}$ for tensor products. The results extend several previous works on Browder spectra.References
- John J. Buoni, A. T. Dash, and Bhushan L. Wadhwa, Joint Browder spectrum, Pacific J. Math. 94 (1981), no. 2, 259–263. MR 628578
- Zoia Ceauşescu and F.-H. Vasilescu, Tensor products and the joint spectrum in Hilbert spaces, Proc. Amer. Math. Soc. 72 (1978), no. 3, 505–508. MR 509243, DOI 10.1090/S0002-9939-1978-0509243-8
- Raúl E. Curto, Connections between Harte and Taylor spectra, Rev. Roumaine Math. Pures Appl. 31 (1986), no. 3, 203–215. MR 847027 —, Applications of several complex variables to multiparameter spectral theory, Survey of Recent Results in Operator Theory, vol. II, J. B. Conway (editor), Longman (to appear).
- Raúl E. Curto and Lawrence A. Fialkow, The spectral picture of $(L_A,R_B)$, J. Funct. Anal. 71 (1987), no. 2, 371–392. MR 880986, DOI 10.1016/0022-1236(87)90010-3
- A. T. Dash, Joint Browder spectra and tensor products, Bull. Austral. Math. Soc. 32 (1985), no. 1, 119–128. MR 811295, DOI 10.1017/S0004972700009783
- Jörg Eschmeier, Tensor products and elementary operators, J. Reine Angew. Math. 390 (1988), 47–66. MR 953676, DOI 10.1515/crll.1988.390.47
- Lawrence A. Fialkow, Spectral properties of elementary operators. II, Trans. Amer. Math. Soc. 290 (1985), no. 1, 415–429. MR 787973, DOI 10.1090/S0002-9947-1985-0787973-9
- Bernhard Gramsch and David Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971), 17–32. MR 291846, DOI 10.1007/BF02052728
- R. E. Harte, Tensor products, multiplication operators and the spectral mapping theorem, Proc. Roy. Irish Acad. Sect. A 73 (1973), 285–302. MR 328642
- M. Putinar, Functional calculus and the Gel′fand transformation, Studia Math. 79 (1984), no. 1, 83–86. MR 772008, DOI 10.4064/sm-79-1-83-86
- M. Schechter and M. Snow, The Fredholm spectrum on tensor products, Proc. Roy. Irish Acad. Sect. A 75 (1975), no. 13, 121–127. MR 377557
- Zbigniew Słodkowski, An infinite family of joint spectra, Studia Math. 61 (1977), no. 3, 239–255. MR 461172, DOI 10.4064/sm-61-3-239-255
- M. Snow, A joint Browder essential spectrum, Proc. Roy. Irish Acad. Sect. A 75 (1975), no. 14, 129–131. MR 385611
- Joseph L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172–191. MR 0268706, DOI 10.1016/0022-1236(70)90055-8
- Joseph L. Taylor, The analytic-functional calculus for several commuting operators, Acta Math. 125 (1970), 1–38. MR 271741, DOI 10.1007/BF02392329 W. Żelazko, Banach algebras, Elsevier, New York, 1973.
- W. Żelazko, An axiomatic approach to joint spectra. I, Studia Math. 64 (1979), no. 3, 249–261. MR 544729, DOI 10.4064/sm-64-3-249-261
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 407-413
- MSC: Primary 47A10; Secondary 47D99
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943057-6
- MathSciNet review: 943057