On summing and related operators acting from a Hilbert space

• Autorzy: Tien N. , Tarieladze V. , Vidal R.
• Języki publikacji: EN

Abstrakty

EN

We study the situation when the behaviour of an operator from a Hilbert space to a Banach space on all orthonormal bases determines whether it belongs to a prescribed class of operators. The cases of (q, 2)-summing, almost summing and [gamma]-summing operators are treated in a unified way.

Słowa kluczowe

EN

bounding operators; converging operators; operator theory; probability measures in Banach spaces; probability theory; random series; stochastic processes; summing operators

PL

miara probabilistyczna w przestrzeniach Banacha; operator ograniczony; procesy stochastyczne; sumowalność operatora; szereg losowy; teoria operatora; teoria prawdopodobieństwa; zbieżność operatora

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 4
• Strony: 365--375
• Opis fizyczny: Bibliogr. 13 poz.,

Twórcy

autor

Tien N.

• Faculty of Mathematics, University of Hanoi, 90 'Nguyen Tr.Ai, Hanoi, Vietnam
• Universidad de Wigo, Departamento de Matematica Aplicada, 36200 Vigo, Espańa

autor

Tarieladze V.

• Muskiielishvili Institute of Computational Mathematics, Georgian Academy of Sciences, Trilisi-93, Republic of Georgia
• Universidad de Vigo, Departamento Dd Matematica Aplicada, 36200 Vigo, Espańa

autor

Vidal R.

• Universidad de Vigo, Departamento de Matematica Aplicada, 36200 Vigo, Espańa

Bibliografia

• [1] J. Diestel, H. Jarchow, A. Tonge, Absolutely Summing Operator Cambridge University Press, 1995.
• [2] W. Słowikowski, Absolutelty 2-summin mappings from and to Hilbert spaces and a Sadakov theorem, Bull. Acad. Polon. Sci., Sęr. sci. math., astronom et phys, 17 (1969) 381-386.
• [3] V. N. Sudakov, On a class of compacts in a Hilbert spacе, Usp. Mat. Nauk. 18 (1963) 181-187.
• [4] N. Тоmсzаk- Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Longmal Scientific Technical, 1989.
• [5] R. M. Dudlеy, Small opеrators between Banach and Hilbert spaces, Studia Math., 38 (1970) 35-41.
• [6] N.N. Vakhania, V.I. Tarieladze, S.A. Chobanyan, Probability Distributions in Banach Spaces, D. Reildel, Dordrecht 1987.
• [7] Т. Liude, A. Pietsch, Mappings Gaussian cylindrical measures in Banach spacеs, Thcory Probab. Appl., 19 (1974) 445-460.
• [8] Nguyen Duy Тien, R. Vidal, Almost, summing operators in Banach spaces, preprint (1995).
• [9] Т. Byczkоwski, Т. Inglot; Gaussian random series on metric vector spaces, Math. Z., 196 (1987) 39-50.
• [10] Nguyen Duy Тien, R. Vidal, On comparison theorems for random series in Banach spaces, preprint (1995).
• [11] P. Halmos, A Hilbert, Space Ргoblem Bookk, Springer-Verlag, second edition, 1982.
• [12] S. Kwаpień, Isomorphic charaterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math., 44 (1972) 583-595.
• [13] М. Мaurеy, G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométrique des espaces de Banach, Studia Math., 48 (1976) 45-90.