Schatten's theorem on absolute Schur algebras
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In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten’s Theorem on the Banach space B(l₂) of bounded linear operators on l₂ involving the duality relation among the class of compact operators K, the trace class C₁ and B(l₂). We also study the reflexivity in such the algebras.
Abstract
In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten’s Theorem on the Banach space B(l₂) of bounded linear operators on l₂ involving the duality relation among the class of compact operators K, the trace class C₁ and B(l₂). We also study the reflexivity in such the algebras.
참고문헌 (5)
- P. Chaisuriya, "Absolute Schur algebras and unbounded matrices", SIAM Journal on Matrix Analysis and Applications, 20(3), pp.596~605 (1999)
- N. Dunford, "Linear Operators. I. General Theory In: Pure and Applied Mathematics, Vol. 7" (1958), Interscience Publishers, Inc.
- L. Livshits, "Banach space duality of absolute Schur algebras", Integral Equations Operator Theory, 41(3), pp.343~359 (2001)
- R. E. Megginson, "An Introduction to Banach Space Theory, Graduate Texts in Mathematics", pp.183~ (1998), Springer-Verlag
- J. Rakbud, "Classes of infinite matrices over Banach algebras", Journal of Mathematical Analysis and Applications, 3(1), pp.31~46 (2005)