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1993 | 107 | 2 | 101-113
Tytuł artykułu

Factorization through Hilbert space and the dilation of L(X,Y)-valued measures

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EN
Abstrakty
EN
We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.
Twórcy
autor
  • Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, U.S.A.
autor
  • Department of Science and Mathematics, GMI Engineering and Management Institute, Flint, Michigan 48504, U.S.A.
Bibliografia
  • [1] S. D. Chatterji, Orthogonally scattered dilation of Hilbert space valued set functions, in: Measure Theory, Oberwolfach 1981, D. Kölzow and D. Maharam-Stone (eds.), Lecture Notes in Math. 945, Springer, New York, 1982, 269-281.
  • [2] J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in $ℒ_p$-spaces and their applications, Studia Math. 29 (1968), 275-326.
  • [3] A. Makagon and H. Salehi, Spectral dilation of operator-valued measures and its application to infinite-dimensional harmonizable processes, ibid. 85 (1987), 257-297.
  • [4] P. Masani, Quasi-isometric measures and their applications, Bull. Amer. Math. Soc. 76 (1970), 427-528.
  • [5] A. G. Miamee, Spectral dilation of L(B,H)-valued measures and its application to stationary dilation for Banach space valued processes, Indiana Univ. Math. J. 38 (1989), 841-860.
  • [6] G. Pisier, Completely bounded maps between sets of Banach space operators, ibid. 39 (1990), 249-277.
  • [7] G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Ser. in Math. 60, Amer. Math. Soc., Providence, R.I., 1986.
  • [8] P. Richard, Harmonizability, V-boundedness, and stationary dilation of Banach-valued processes, in: Probability in Banach Spaces, 8, Proc. Eighth Internat. Conf., R. Dudley, M. Hahn and J. Kuelbs (eds.), Birkhäuser, Boston, 1992, 189-205.
  • [9] M. Rosenberg, Quasi-isometric dilations of operator-valued measures and Grothendieck's inequality, Pacific J. Math. 103 (1982), 135-161.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv107i2p101bwm
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