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Lumer, G.

Semi-inner-product spaces. (English) Zbl 0102.32701

Trans. Am. Math. Soc. 100, 29-43 (1961).
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Cited in 12 Reviews
Cited in 239 Documents

Keywords:

functional analysis
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References:

[1] S. Banach, Théorie des operations linéaires, Warszawa, 1932. · JFM 58.0420.01
[2] H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. (2) 62 (1955), 217 – 229. · Zbl 0067.35002 · doi:10.2307/1969676
[3] Masanori Fukamiya, On a theorem of Gelfand and Neumark and the \?*-algebra, Kumamoto J. Sci. Ser. A. 1 (1952), no. 1, 17 – 22. · Zbl 0049.08605
[4] I. Gelfand and M. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 197 – 213 (English, with Russian summary). · Zbl 0060.27006
[5] Paul R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, AMS Chelsea Publishing, Providence, RI, 1998. Reprint of the second (1957) edition. · Zbl 0962.46013
[6] Paul R. Halmos, Günter Lumer, and Juan J. Schäffer, Square roots of operators, Proc. Amer. Math. Soc. 4 (1953), 142 – 149. · Zbl 0050.34004
[7] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[8] Richard V. Kadison, Isometries of operator algebras, Ann. Of Math. (2) 54 (1951), 325 – 338. · Zbl 0045.06201 · doi:10.2307/1969534
[9] I. Kaplansky, Topological algebra, Notas Mat. No. 16 (1959), v+87. · Zbl 0092.32002
[10] Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953. · Zbl 0052.11701
[11] G. Lumer, Fine structure and continuity of spectra in Banach algebras, An. Acad. Brasil. Ci. 26 (1954), 229 – 233. · Zbl 0057.10101
[12] Ivan Vidav, Eine metrische Kennzeichnung der selbstadjungierten Operatoren, Math. Z. 66 (1956), 121 – 128 (German). · Zbl 0071.11503 · doi:10.1007/BF01186601
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