Almost sure approximation of unbounded operators in L 2 ( X , A , μ )

Ryszard Jajte; Adam Paszkiewicz

Studia Mathematica (1998)

  • Volume: 128, Issue: 2, page 103-120
  • ISSN: 0039-3223

Abstract

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The possibilities of almost sure approximation of unbounded operators in L 2 ( X , A , μ ) by multiples of projections or unitary operators are examined.

How to cite

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Jajte, Ryszard, and Paszkiewicz, Adam. "Almost sure approximation of unbounded operators in $L_2 (X,A,μ)$." Studia Mathematica 128.2 (1998): 103-120. <http://eudml.org/doc/216477>.

@article{Jajte1998,
abstract = {The possibilities of almost sure approximation of unbounded operators in $L_2(X,A,μ)$ by multiples of projections or unitary operators are examined.},
author = {Jajte, Ryszard, Paszkiewicz, Adam},
journal = {Studia Mathematica},
keywords = {$L_2(X,A,μ)$; unbounded operators; almost sure convergence; projections; unitary operators; approximation; almost sure approximation of unbounded operators; multiples of projections},
language = {eng},
number = {2},
pages = {103-120},
title = {Almost sure approximation of unbounded operators in $L_2 (X,A,μ)$},
url = {http://eudml.org/doc/216477},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Jajte, Ryszard
AU - Paszkiewicz, Adam
TI - Almost sure approximation of unbounded operators in $L_2 (X,A,μ)$
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 2
SP - 103
EP - 120
AB - The possibilities of almost sure approximation of unbounded operators in $L_2(X,A,μ)$ by multiples of projections or unitary operators are examined.
LA - eng
KW - $L_2(X,A,μ)$; unbounded operators; almost sure convergence; projections; unitary operators; approximation; almost sure approximation of unbounded operators; multiples of projections
UR - http://eudml.org/doc/216477
ER -

References

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  1. [1] J. L. Ciach, R. Jajte and A. Paszkiewicz, On the almost sure approximation of self-adjoint operators in L 2 ( 0 , 1 ) , Math. Proc. Cambridge Philos. Soc. 119 (1996), 537-543. Zbl0846.47011
  2. [2] J. L. Ciach, R. Jajte and A. Paszkiewicz, On the almost sure approximation and convergence of linear operators in L 2 -spaces, Probab. Math. Statist. 15 (1995), 215-225. Zbl0859.60027
  3. [3] P. R. Halmos, Two subspaces, Trans. Amer. Math. Soc. 144 (1969), 381-389. Zbl0187.05503
  4. [4] R. Jajte and A. Paszkiewicz, Topics in almost sure approximation of operators in L 2 -spaces, in: Interaction between Functional Analysis, Harmonic Analysis, and Probability (Columbia, Mo., 1994), N. Kalton, E. Saab and S. M. Montgomery-Smith (eds.), Lecture Notes in Pure and Appl. Math. 175, M. Dekker, New York, 1996, 219-228. Zbl0874.47008
  5. [5] M. Loève, Probability Theory. II, Springer, New York, 1978. 
  6. [6] J. Marcinkiewicz, Sur la convergence de séries orthogonales, Studia Math. 6 (1933), 39-45. Zbl62.0284.01
  7. [7] A. Paszkiewicz, Convergences in W*-algebras, J. Funct. Anal. 69 (1986), 143-154. Zbl0612.46060
  8. [8] Ş. Strătilă and L. Zsidó, Lectures on von Neumann Algebras, Editura Academiei, Bucureşti, 1979. 
  9. [9] M. Takesaki, Theory of Operator Algebras, I, Springer, Berlin, 1979. 

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