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On the almost sure approximation of self-adjoint operators in L2 (0, 1)

Published online by Cambridge University Press:  24 October 2008

L. J. Ciach ,
R. Jajte  and
A. Paszkiewicz
L. J. Ciach
Affiliation:
Institute of Mathematics, Lódź University, UL Stefana Banacha 22, 90–238 Lódź, Poland
R. Jajte
Affiliation:
Institute of Mathematics, Lódź University, UL Stefana Banacha 22, 90–238 Lódź, Poland
A. Paszkiewicz
Affiliation:
Institute of Mathematics, Lódź University, UL Stefana Banacha 22, 90–238 Lódź, Poland
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Extract

There are several important theorems concerning the almost sure convergence of (monotone) sequences of orthogonal projections in L2-spaces. Let us mention here the martingale convergence theorems or the results on the developments of functions with respect to orthogonal systems. On the other hand every self-adjoint operator with the spectrum on the interval [0, 1] is a limit of some sequence of orthogonal projections in the weak operator topology (see [1]). This paper is devoted to a problem of approximation of a self-adjoint operator A acting in L2 (0, 1) by a sequence Pn of orthogonal projections in the sense that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 3 , April 1996 , pp. 537 - 543
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Kadison, R. V. and Ringrose, J. R.. Fundamentals of the theory of operator algebras, vols. I, II (Academic Press, 1983).Google Scholar
[2]Marcinkiewicz, J.. Sur la convergence de séries orthogonales. Studia Math. 6 (1936), 39–45.CrossRefGoogle Scholar
[3]Nelson, E.. Notes on non-commutative integration. J. Funct. Anal. 15 (1974), 103–116.CrossRefGoogle Scholar
[4]Padmanabhan, A. R.. Stability and mixing in von Neumann algebras. Kodai Math. Sem. Rep 18 (1966), 335–342.CrossRefGoogle Scholar
[5]Paszkiewicz, A.. Measures on projectors in W*-factors. J. Funct. Anal. 69 (1986), 87–117.Google Scholar
[6]Paszkiewicz, A.. Convergence in W*-algebras. J. Funct. Anal. 90 (1990), 143–154.CrossRefGoogle Scholar
[7]Renyi, A.. On mixing sequences of sets. Acta Mathematica 9 (1959), 1–2.Google Scholar