Almost sure approximation of unbounded operators in $L_2 (X,A,μ)$

ArticleOriginal scientific text

Title

Authors ¹, ¹

The possibilities of almost sure approximation of unbounded operators in

L_{2} (X, A, μ)

by multiples of projections or unitary operators are examined.

L_{2} (X, A, μ)

, unbounded operators, almost sure convergence, projections, unitary operators, approximation

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