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Molnár, Lajos

Modular bases in a Hilbert \(A\)-module. (English) Zbl 0809.46039

Czech. Math. J. 42, No. 4, 649-656 (1992).
Summary: Following M. Ozawa [Kodai Math. J. 3, 26-39 (1980; Zbl 0435.60033)] we introduce the concept of a modular base in a Hilbert \(A\)-module and prove that the cardinalities of any two such bases are the same.

Cited in 3 Documents

MSC:

46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Keywords:

modular bases; Hilbert \(A\)-module

Citations:

Zbl 0435.60033
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\textit{L. Molnár}, Czech. Math. J. 42, No. 4, 649--656 (1992; Zbl 0809.46039)
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References:

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[2] S. A. Gaal: Linear analysis and representation theory. Springer-Verlag, Berlin, 1973. · Zbl 0275.43008
[3] L. Molnár: On Saworotnow’s Hilbert \(A\)-modules. · Zbl 0818.46056
[4] M. Ozawa: Hilbert \(B(H)\)-modules and stationary processes. Kodai Math. J. 3 (1980), 26-39. · Zbl 0435.60033 · doi:10.2996/kmj/1138036115
[5] P. P. Saworotnow: A generalized Hilbert space. Duke Math. J. 35 (1968), 191-197. · Zbl 0161.33403 · doi:10.1215/S0012-7094-68-03520-5
[6] P. P. Saworotnow and J. C. Friedell: Trace-class for an arbitrary \(H^*\)-algebra. Proc. Amer. Math. Soc. 26 (1970), 95-100. · Zbl 0197.39701 · doi:10.2307/2036810
[7] P. P. Saworotnow: Trace-class and centralizers of an \(H^*\)-algebra. Proc. Amer. Math. Soc. 26 (1970), 101-104. · Zbl 0197.39702 · doi:10.2307/2036811
[8] J. F. Smith: The \(p\)-classes of an \(H^*\)-algebra. Pacific J. Math. 42 (1972), 777-793. · Zbl 0247.46065 · doi:10.2140/pjm.1972.42.777
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