Absolutely summing holomorphic mappings. (English) Zbl 0854.46042

Matos, Mário C.

An. Acad. Bras. Ciênc. 68, No. 1, 1-13 (1996).

Summary: For complex Banach spaces \(E\), \(F\) and \(s,r\in [1,+ \infty]\) we consider the concept of absolutely \((s;r)\)-summing entire mappings from \(E\) into \(F\). Several results and examples show that the existence of such mappings is not a rare fact. We study the possibility of factorization results through \(L_p\) spaces for these mappings.

MSC:

46G20	Infinite-dimensional holomorphy
47B10	Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)

Keywords:

absolutely summing polynomials on Banach spaces; holomorphic mappings of dominated type; absolutely \((s; r)\)-summing entire mappings; factorization results through \(L_ p\) spaces