In this paper we provide a unifying approach to the study of Banach ideals of linear and multilinear operators defined, or characterized, by the transformation of vector-valued sequences. We investigate and apply the linear and multilinear stabilities of some frequently used classes of vector-valued sequences.
In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.
Given an operator ideal I, we study the multi-ideal I • L and the polynomial ideal I • P. The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained. §1. Introduction Since the 1983 paper by A. Pietsch [26], ideals of multilinear mappings (multi-ideals) and homogeneous polynomials (polynomial ideals) between Banach spaces have been studied as a natural consequence of the successful theory of operator ideals. Several ideals have been investigated and abstract methods to generate ideals of multilinear mappings and polynomials have been introduced (see [6,20]
In this paper we use Nachbin's holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables.
In this paper we use complex interpolation to obtain new inclusion and coincidence theorems for absolutely and multiple summing multilinear mappings between Banach spaces. In particular, we derive optimal coincidence theorems of Bohnenblust-Hille type for multilinear forms on K-convex Banach spaces of cotype 2.
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