The double centralizer algebra as a linear space
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- by Robert A. Fontenot PDF
- Proc. Amer. Math. Soc. 53 (1975), 99-103 Request permission
Abstract:
Let $A$ be a ${C^{\ast }}$-algebra and $M(A)$ be the double centralizer algebra of $A$. The properties semireflexivity, nuclearity, $({\text {DF)}}$, and strict compactness of the unit ball are characterized in $M(A)$ endowed with the strict topology.References
- R. Creighton Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95–104. MR 105611
- Robert C. Busby, Double centralizers and extensions of $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 132 (1968), 79–99. MR 225175, DOI 10.1090/S0002-9947-1968-0225175-5
- Heron S. Collins, On the space $l^{\infty }\,(S)$, with the strict topology, Math. Z. 106 (1968), 361–373. MR 239406, DOI 10.1007/BF01115085
- H. S. Collins and J. R. Dorroh, Remarks on certain function spaces, Math. Ann. 176 (1968), 157–168. MR 222644, DOI 10.1007/BF02056983
- H. S. Collins and W. H. Summers, Some applications of Hewitt’s factorization theorem, Proc. Amer. Math. Soc. 21 (1969), 727–733. MR 240636, DOI 10.1090/S0002-9939-1969-0240636-7 J. Dixmier, Les ${C^{\ast }}$-algèbres et leur représentations, 2ième éd., Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1969. MR 39 #7442.
- Edwin Hewitt, The ranges of certain convolution operators, Math. Scand. 15 (1964), 147–155. MR 187016, DOI 10.7146/math.scand.a-10738
- Edith A. McCharen, A characterization of dual $B^{\ast }$-algebras, Proc. Amer. Math. Soc. 37 (1973), 84. MR 306927, DOI 10.1090/S0002-9939-1973-0306927-7 H. H. Schaeffer, Topological vector spaces, McMillan, New York, 1966. MR 33 #1689.
- F. Dennis Sentilles and Donald Curtis Taylor, Factorization in Banach algebras and the general strict topology, Trans. Amer. Math. Soc. 142 (1969), 141–152. MR 247437, DOI 10.1090/S0002-9947-1969-0247437-9
- W. H. Summers, Factorization in Fréchet spaces, Studia Math. 39 (1971), 209–216. MR 306911, DOI 10.4064/sm-39-2-209-216
- Donald Curtis Taylor, A general Phillips theorem for $C^{^{\ast } }$-algebras and some applications, Pacific J. Math. 40 (1972), 477–488. MR 308799
- Donald Curtis Taylor, The strict topology for double centralizer algebras, Trans. Amer. Math. Soc. 150 (1970), 633–643. MR 290117, DOI 10.1090/S0002-9947-1970-0290117-2
- B. J. Tomiuk and Pak-ken Wong, The Arens product and duality in $B^{\ast }$-algebras, Proc. Amer. Math. Soc. 25 (1970), 529–535. MR 259620, DOI 10.1090/S0002-9939-1970-0259620-0
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 99-103
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0407613-7
- MathSciNet review: 0407613