BOUNDED LINEAR OPERATORS ON BANACH FUNCTION SPACES OF VECTOR-VALUED FUNCTIONS

@inproceedings{GRETSKY2010BOUNDEDLO,
  title={BOUNDED LINEAR OPERATORS ON BANACH FUNCTION SPACES OF VECTOR-VALUED FUNCTIONS},
  author={N. E. GRETSKY},
  year={2010}
}
  • N. E. GRETSKY
  • Published 2010
Representations of bounded linear operators on Banach function spaces of vector-valued functions to Banach spaces are given in terms of operator-valued measures. Then spaces whose duals are Banach function spaces are characterized. With this last information, reflexivity of this type of space is discussed. Finally, the structure of compact operators on these spaces is studied, and an observation is made on the approximation problem in this context. 

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Showing 1-10 of 15 references

Banach function spaces of vector-valued functions, M.S

S. E. Mills
Baton Rouge, La., • 1970
View 5 Excerpts
Highly Influenced

Some remarks on Banach function spaces, Nederl

W.A.J. Luxemburg, A. C. Zaanen
Akad. Wetensch. Proc. Ser. A • 1956
View 6 Excerpts
Highly Influenced

Luxemburg, Banach function spaces, Thesis

A J.W.
1955
View 7 Excerpts
Highly Influenced

On compact sets of compact operators, Ann

K. Vala
MR • 1964
View 3 Excerpts
Highly Influenced

Functional analysis and semi-groups, rev

E. Hille, R. S. Phillips
ed., Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc, Providence, R. I., 1957. MR 19, 664. License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use • 1972
View 1 Excerpt

Projecting the space of bounded operators onto the space of compact operators

A. Tong
Proc. Amer. Math. Soc • 1970

Gretsky, Representation theorems on Banach function spaces, Mem

N E.
Amer. Math. Soc. No • 1968
View 2 Excerpts

Martingale convergence and the Radon-Nikodym theorem in Banach spaces

S. D. Chatterji
Math. Scand • 1968

Integration, rev

A. C. Zaanen
ed., North-Holland, Amsterdam; Interscience, New York, • 1967