Strong l p sequences, Weak l p sequences, Characterization of p-summing operators CONSTRUCTIONS OF P-SUMMING OPERATORS Finite rank operators, The Banach ideal of p-summing operators, Injectivity, Inclusion Theorem BASIC EXAMPLES ,40 Multiplication operators, Formal inclusion operators, Diagonal operators, Embeddings of function spaces, Kernel operators DOMINATION AND FACTORIZATION \ Pietsch Domination Theorem, Pietsch Factorization Theorem, Operators from and to C(K')-spaces, 2-summing operators SOME CONSEQUENCES Weak compactness and complete continuity of p-summing operators, Weak Dvoretzky-Rogers Theorem, p-summing character of biadjoints and adjoints COMPOSITION \ NOTES AND REMARKS 3. Summing Operators on £ P-Spaces £p-SPACES Operators from £i-spaces to £2-spaces are 1-summing, Approximation in L p (ii) and C(K), Lp(ji) and C(K) as basic examples of £ p-spaces OPERATORS ON £OO-SPACES Operators from Coo-spaces to £ p-spaces (l
The aim of this paper is to investigate close relations between the validity of Hahn-Banach extension theorems for multilinear forms on Banach spaces and summability properties of sequences from these spaces. A case of particular importance occurs when we consider Banach spaces which have the property that every bilinear form extends to any superspace.
A well-known result of Rosenthal [7] states that every reflexive quotient of a space ~(K) is super-reflexive; in fact, it appears as a quotient of ~eq(/z) for some 2 O a number N(e)>O such that l [ rxll
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