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We give conditions so that a polynomial be factorable through an L_r(μ) space. Among them, we prove that, given a Banach space X and an index m, every absolutely summing operator on X is 1-factorable if and only if every 1-dominated m-homogeneous polynomial on X is right 1-factorable, if and only if every 1-dominated m-homogeneous polynomial on X is left 1-factorable. As a consequence, if X has local unconditional structure, then every 1-dominated homogeneous polynomial on X is right and left 1-factorable.
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참고문헌 (22)
참고문헌 신청
A. Defant / 1993 / Tensor Norms and Operator Ideals, North-Holland Mathematics Studies / North-Holland Publishing Co.
D. Carando / 1999 / Extendible polynomials on Banach spaces / J. Math. Anal. Appl. 233 (1) : 359 ~ 372
F. Blasco / 1997 / Complementation in spaces of symmetric tensor products and polynomials / Studia Math. 123 (2) : 165 ~ 173
G. Botelho / 2005 / Two new properties of ideals of polynomials and applications / Indag. Math. 16 (2) : 157 ~ 169
G. Botelho / 2006 / Ideals of polynomials generated by weakly compact operators / Note Mat. 25 (1) : 69 ~ 105
D. Carando / 1999 / Extendible polynomials on Banach spaces / J. Math. Anal. Appl. 233 (1) : 359 ~ 372
F. Blasco / 1997 / Complementation in spaces of symmetric tensor products and polynomials / Studia Math. 123 (2) : 165 ~ 173
G. Botelho / 2005 / Two new properties of ideals of polynomials and applications / Indag. Math. 16 (2) : 157 ~ 169
G. Botelho / 2006 / Ideals of polynomials generated by weakly compact operators / Note Mat. 25 (1) : 69 ~ 105
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