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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce weak$^{^*}$ to norm continuous maps to $l^p $ space $ (p\in (1, \infty))$. Versions of H\"older's inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the $l^p$ spaces and the well-known classical theorems follow from our results.
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참고문헌 (9)
참고문헌 신청
E.M. Alfsen / 1972 / Structure in real Banach spaces / Ann. Math 96:98~173
J Diestel / 2008 / The Metric Theory of Tensor Products:Grothendieck's Resume Revisited
J. Dixmier / 1950 / Les fonctionnelles lin'earies sur l'ensemble des operateurs bornes dans espace de Hilbert / Ann. Math 51:387~408
P. Harmand / 1993 / Lecture Notes in Mathematics, vol. 1547 / Springer-Verlag
R.V. Kadison / 1983 / Fundamentals of the Theory of Operator Al-gebras, vol. I / Academic Press
J Diestel / 2008 / The Metric Theory of Tensor Products:Grothendieck's Resume Revisited
J. Dixmier / 1950 / Les fonctionnelles lin'earies sur l'ensemble des operateurs bornes dans espace de Hilbert / Ann. Math 51:387~408
P. Harmand / 1993 / Lecture Notes in Mathematics, vol. 1547 / Springer-Verlag
R.V. Kadison / 1983 / Fundamentals of the Theory of Operator Al-gebras, vol. I / Academic Press
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