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

• Autorzy: Ryszard Jajte , Adam Paszkiewicz
• Języki publikacji: EN

Abstrakty

EN

The possibilities of almost sure approximation of unbounded operators in $L_2(X,A,μ)$ by multiples of projections or unitary operators are examined.

Słowa kluczowe

EN

$L_2(X,A,μ)$; unbounded operators; almost sure convergence; projections; unitary operators; approximation

Kategorie tematyczne

• 47A58: Operator approximation theory
• 60F15: Strong theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 128
• Numer: 2
• Strony: 103-120

Daty

wydano

1998

otrzymano

1997-06-17

poprawiono

1997-07-23

Twórcy

autor

Ryszard Jajte

• Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

autor

Adam Paszkiewicz

• Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [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.
• [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.
• [3] P. R. Halmos, Two subspaces, Trans. Amer. Math. Soc. 144 (1969), 381-389.
• [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.
• [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.
• [7] A. Paszkiewicz, Convergences in W*-algebras, J. Funct. Anal. 69 (1986), 143-154.
• [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.