On locally Hilbert spaces

• Autorzy: Gheondea A.

Identyfikatory

DOI

10.7494/OpMath.2016.36.6.735

• Języki publikacji: EN

Abstrakty

EN

This is an investigation of some basic properties of strictly inductive limits of Hilbert spaces, called locally Hilbert spaces, with respect to their topological properties, the geometry of their subspaces, linear functionals and dual spaces.

Słowa kluczowe

EN

locally Hilbert space; inductive limit; projective limit; orthocomplemented subspaces; linear functional; dual spaces

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 6
• Strony: 735--747
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Gheondea A.

• Bilkent University Department of Mathematics 06800 Bilkent, Ankara, Turkey Institutul de Matematica al Academiei Romane C.P. 1-764, 014700 Bucuresti, Romania

Bibliografia

• [1] G. Allan, On a class of locally convex algebras, Proc. London Math. Soc. 15 (1965), 399-421.
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• [3] J. Bognar, Indefinite Inner Product Spaces, Springer Verlag, Berlin 1974.
• [4] A. Gheondea, Operator models for Hilbert locally C* -modules, arXiv: 1507.07643 [math.OA].
• [5] A. Grothendieck, Topological Vector Spaces, Gordon and Breach, Montreux 1973.
• [6] S. Gudder, Inner product spaces, Amer. Math. Month. 81 (1974), 29-36.
• [7] A. Inoue, Locally C*-algebras, Mem. Fac. Sci. Kyushu Univ. Ser. A, 25 (1971), 197-235.
• [8] M. Joitja, Locally von Neumann algebras, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 42 (1999) 90, 51-64.
• [9] R. V. Kadison, J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, Volume I: Elementary Theory, Graduate Studies in Mathematics, vol. 15, Amer. Math. Soc, 1997.
• [10] Y. Komura, Some examples on locally convex spaces, Math. Annalen 153 (1964), 150-162. [11] G. Kóthe, Topological Vector Spaces I, Second edition, Springer-Verlag, Berlin 1983.
• [12] R. Meise, D. Vogt, Introduction to Functional Analysis, Oxford University Press, Oxford 1997.
• [13] N.C. Phillips, Inverse limits of C*-algebras, J. Operator Theory 19 (1988), 159-195. [14] K. Schmudgen, Uber LMC*-Algebren, Math. Nachr. 68 (1975), 167-182.
• [15] D. Voiculescu, Dual algebraic structures on operator algebras related to free products, J. Operator Theory 17 (1987), 85-98.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.