Definable Operators on Hilbert Spaces

Isaac Goldbring
Source: Notre Dame J. Formal Logic Volume 53, Number 2 (2012), 193-201.

Abstract

Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.

First Page:
Primary Subjects: 03C40
Secondary Subjects: 47A05
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1336588250
Digital Object Identifier: doi:10.1215/00294527-1715689
Mathematical Reviews number (MathSciNet): MR2925277
Zentralblatt MATH identifier: 06054425

References

Argyros, S. A., and R. G. Haydon, "A hereditarily indecomposable $\mathcal{L}_\infty$"-space that solves the scalar-plus-compact problem, Acta Mathematica, vol. 206 (2011), pp. 1–54.
Mathematical Reviews (MathSciNet): MR2784662
Zentralblatt MATH: 1223.46007
Digital Object Identifier: doi:10.1007/s11511-011-0058-y
Conway, J. B., A Course in Functional Analysis, 2nd edition, vol. 96 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1990.
Mathematical Reviews (MathSciNet): MR1070713
Zentralblatt MATH: 0706.46003
Goldbring, I., "An approximate Herbrand's theorem and definable functions in metric structures", forthcoming in Mathematical Logic Quarterly.
Goldbring, I., "Definable functions in Urysohn's metric space", forthcoming in Illinois Journal of Mathematics.
Gowers, T., http://gowers.wordpress.com/2009/02/07.
Yaacov, I. B., A. Berenstein, C. W. Henson, and A. Usvyatsov, "Model theory for metric structures", pp. 315–427 in Model Theory with Applications to Algebra and Analysis. Vol. 2, edited by Z. Chatzidakis, D. Macpherson, A. Pillay, and A. Wilkie, vol. 350 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 2008.
Mathematical Reviews (MathSciNet): MR2446305
Zentralblatt MATH: 1233.03045