# Almost sure approximation of unbounded operators in ${L}_{2}(X,A,\mu )$

Ryszard Jajte; Adam Paszkiewicz

Studia Mathematica (1998)

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

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topJajte, 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

top- [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] 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] P. R. Halmos, Two subspaces, Trans. Amer. Math. Soc. 144 (1969), 381-389. Zbl0187.05503
- [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] M. Loève, Probability Theory. II, Springer, New York, 1978.
- [6] J. Marcinkiewicz, Sur la convergence de séries orthogonales, Studia Math. 6 (1933), 39-45. Zbl62.0284.01
- [7] A. Paszkiewicz, Convergences in W*-algebras, J. Funct. Anal. 69 (1986), 143-154. Zbl0612.46060
- [8] Ş. Strătilă and L. Zsidó, Lectures on von Neumann Algebras, Editura Academiei, Bucureşti, 1979.
- [9] M. Takesaki, Theory of Operator Algebras, I, Springer, Berlin, 1979.

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