Conditional Banach Spaces, Conditional Projections and Generalized Martingales.
نویسندگان
چکیده
منابع مشابه
Conditional Expectation and Martingales
This is a set of very hurriedly compiled notes. It has not been proof-checked and is likely to have some errors. These, though, should be minor errors and maybe cleared up by referring to the relevant texts. The texts that have been used in the preparation of the notes are Feller; Grimmett and Stirzaker; Goswami and Rao; David Williams; and Mitzenmacher and Upfal. The purpose behind the notes i...
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These notes are intended to introduce concentration inequalities for martingales with bounded increments. The final section also provides a gentle introduction to conditional expectation based on sigma fields. In contrast to providing a firm foundation for measure-theoretic probability, the primary goal is to introduce the language and intuition used in the study of martingales. The presentatio...
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A fundamental question in operator theory is: how rich is the collection of oprrators on a given Banach space? For classical spaces, especially Hilbert space, a well developed theory of operators exists. However a Banach space may have far fewer operators than one might expect. Shelah [S] has constructed a nonseparable Ba~lach space X , for which the space of operators with separable range has ...
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Increasing sequences of contractive projections on a reflexive LP space share an unconditionality property similar to that exhibited sequences of self-adjoint projections on a Hilbert space. A slight variation of this property is shown to be precisely the correct condition on a reflexive Banach space to ensure that every operator with a contractive AC-functional calculus is scalar-type spectraL
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In this note we investigate generalized projections in Banach algebras. Our results generalize results obtained for bounded linear operators on Hilbert spaces.
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1970
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11001