A characterization of Hilbert-Schmidt operators
A. Pełczyński (1967)
Studia Mathematica
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A. Pełczyński (1967)
Studia Mathematica
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Zbigniew Pasternak-Winiarski (1998)
Studia Mathematica
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We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.
J. Holub (1972)
Studia Mathematica
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Gideon Schechtman (1987)
Compositio Mathematica
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S. Kwapień (1972)
Studia Mathematica
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Jari Taskinen (1988)
Studia Mathematica
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Stanisław Kwapień, Stanisław Szarek (1979)
Studia Mathematica
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Carsten Schütt (1982)
Compositio Mathematica
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Y. Gordon, O. Guédon, M. Meyer (1998)
Studia Mathematica
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We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex. ...
Stanisław Kwapień, Carsten Schütt (1985)
Studia Mathematica
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