A minimax formula for dual $B^*$-algebras
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- by Pak Ken Wong PDF
- Trans. Amer. Math. Soc. 224 (1976), 281-298 Request permission
Abstract:
Let A be a dual ${B^\ast }$-algebra. We give a minimax formula for the positive elements in A. By using this formula and some of its consequent results, we introduce and study the symmetric norms and symmetrically-normed ideals in A.References
- Bruce Alan Barnes, A generalized Fredholm theory for certain maps in the regular representations of an algebra, Canadian J. Math. 20 (1968), 495–504. MR 232208, DOI 10.4153/CJM-1968-048-2
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
- I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142, DOI 10.1090/mmono/018
- Alfred Horn, On the singular values of a product of completely continuous operators, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 374–375. MR 45316, DOI 10.1073/pnas.36.7.374
- Tôzirô Ogasawara and Kyôichi Yoshinaga, Weakly completely continuous Banach $^*$-algebras, J. Sci. Hiroshima Univ. Ser. A 18 (1954), 15–36. MR 70068
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
- Robert Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 27, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0119112, DOI 10.1007/978-3-642-87652-3
- Pak Ken Wong, Modular annihilator $A^{\ast }$-algebras, Pacific J. Math. 37 (1971), 825–834. MR 305083, DOI 10.2140/pjm.1971.37.825
- Pak Ken Wong, On the Arens products and certain Banach algebras, Trans. Amer. Math. Soc. 180 (1973), 437–448. MR 318885, DOI 10.1090/S0002-9947-1973-0318885-4
- Pak Ken Wong, The $p$-class in a dual $B^{\ast }$-algebra, Trans. Amer. Math. Soc. 200 (1974), 355–368. MR 358371, DOI 10.1090/S0002-9947-1974-0358371-X —, On certain subalgebras of a dual ${B^\ast }$-algebra, J. Australian Math. Soc. (to appear).
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 224 (1976), 281-298
- MSC: Primary 46K05
- DOI: https://doi.org/10.1090/S0002-9947-1976-0428047-0
- MathSciNet review: 0428047