Displaying similar documents to “Quadratic forms on linearly topologized vector spaces”

Hereditarily finitely decomposable Banach spaces

V. Perenczi (1997)

Studia Mathematica

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A Banach space is said to be H D n if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of H D n spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex H D n , then dim ( ℒ ( X ) / S ( X ) ) ≤ n 2 , where S(X) denotes the space of strictly singular operators on X. It follows that if X is a real hereditarily indecomposable space, then ℒ(X)/S(X) is a division ring isomorphic either to ℝ, ℂ, or ℍ, the quaternionic...