Banach Spaces with Many Projections
نویسندگان
چکیده
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 codimension one in B(.Y). An interesting open problem is whether there is a Banach space X for which the space of compact operators has finite codimension in B ( X ) .
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