Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-27T08:32:37.097Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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