Orthogonal sums in Kreĭn spaces

Rovnyak, James

doi:10.1090/proc/14718

Orthogonal sums in Kreĭn spaces
HTML articles powered by AMS MathViewer

by James Rovnyak

Proc. Amer. Math. Soc. 149 (2021), 1999-2010

DOI: https://doi.org/10.1090/proc/14718

Published electronically: February 24, 2021

PDF | Request permission

Abstract:

Infinite orthogonal families of regular subspaces of a Kreĭn space exhibit a wide range of behavior. An elementary method is used to show that conditions on sums of projections produce behavior similar to that of orthogonal closed subspaces of a Hilbert space.

References

T. Ya. Azizov and I. S. Iokhvidov, Linear operators in spaces with an indefinite metric, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1989. Translated from the Russian by E. R. Dawson; A Wiley-Interscience Publication. MR 1033489
János Bognár, Indefinite inner product spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 78, Springer-Verlag, New York-Heidelberg, 1974. MR 0467261, DOI 10.1007/978-3-642-65567-8
Michael A. Dritschel and James Rovnyak, Operators on indefinite inner product spaces, Lectures on operator theory and its applications (Waterloo, ON, 1994) Fields Inst. Monogr., vol. 3, Amer. Math. Soc., Providence, RI, 1996, pp. 141–232. MR 1364446
Aurelian Gheondea, On the geometry of pseudoregular subspaces of a Kreĭn space, Spectral theory of linear operators and related topics (Timişoara/Herculane, 1983) Oper. Theory Adv. Appl., vol. 14, Birkhäuser, Basel, 1984, pp. 141–156. MR 789614
Paul R. Halmos, Introduction to Hilbert Space and the theory of Spectral Multiplicity, Chelsea Publishing Co., New York, N. Y., 1951. MR 0045309
G. Mackey, Commutative Banach algebras, multigraphed Harvard lecture notes, by A. Blair, 1952.
Alejandra Maestripieri and Francisco Martínez Pería, Normal projections in Krein spaces, Integral Equations Operator Theory 76 (2013), no. 3, 357–380. MR 3065299, DOI 10.1007/s00020-013-2063-3
Brian W. McEnnis, Shifts on indefinite inner product spaces, Pacific J. Math. 81 (1979), no. 1, 113–130. MR 543738, DOI 10.2140/pjm.1979.81.113
Brian W. McEnnis, Shifts on indefinite inner product spaces. II, Pacific J. Math. 100 (1982), no. 1, 177–183. MR 661447, DOI 10.2140/pjm.1982.100.177
Brian W. McEnnis, Shifts on Kreĭn spaces, Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 201–211. MR 1077439, DOI 10.1090/pspum/051.2/1077439
John Wermer, Commuting spectral measures on Hilbert space, Pacific J. Math. 4 (1954), 355–361. MR 63564, DOI 10.2140/pjm.1954.4.355