Unital multiplications on a Hilbert space

Froelich, John

doi:10.1090/S0002-9939-1993-1116259-8

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

Unital multiplications on a Hilbert space

Author: John Froelich
Journal: Proc. Amer. Math. Soc. 117 (1993), 757-759
MSC: Primary 46H20; Secondary 47D25
MathSciNet review: 1116259
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Abstract: We provide a new proof of two theorems of Ingelstam that identify the Hilbert spaces with a unital multiplication satisfying $\vert\vert xy\vert\vert \leqslant \vert\vert x\vert\vert\,\vert\vert y\vert\vert$ and $\vert\vert 1\vert\vert = 1$ .

[1] H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. (2) 62 (1955), 217–229. MR 0071733 (17,177a)
[2] John Froelich, Strictly cyclic operator algebras, Trans. Amer. Math. Soc. 325 (1991), no. 1, 73–86. MR 989575 (91h:47043), http://dx.doi.org/10.1090/S0002-9947-1991-0989575-0
[3] Lars Ingelstam, A vertex property for Banach algebras with identity, Math. Scand. 11 (1962), 22–32. MR 0146679 (26 #4199)
[4] Lars Ingelstam, Hilbert algebras with identity, Bull. Amer. Math. Soc. 69 (1963), 794–796. MR 0154145 (27 #4096), http://dx.doi.org/10.1090/S0002-9904-1963-11035-6
[5] Alan Lambert, Strictly cyclic operator algebras, Pacific J. Math. 39 (1971), 717–726. MR 0310664 (46 #9762)
[6] 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 (22 #5903)
[7] Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York, 1973. McGraw-Hill Series in Higher Mathematics. MR 0365062 (51 #1315)
[8] Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. Math. Surveys, No. 13. MR 0361899 (50 #14341)
[9] M. F. Smiley, Real Hilbert algebras with identity, Proc. Amer. Math. Soc. 16 (1965), 440–441. MR 0176316 (31 #591), http://dx.doi.org/10.1090/S0002-9939-1965-0176316-2

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