Limit semigroups of Bernstein-Schnabl operators associated with positive projections
By using the concepts of limited -converging operators between two Banach spaces and , -sets and -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as -Dunford–Pettis property of order and Pelczyński’s property of order , .
This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show that the...
The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established....
2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94.New concepts of linear colligations and dynamic systems, corresponding to the linear operators, acting in the Banach spaces, are introduced. The main properties of the transfer function and its relation to the dual transfer function are established.
Mathematics Subject Classification: 26A33, 47A60, 30C15.In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.
The space of inessential bounded linear operators from one Banach space into another is introduced. This space, , is a subspace of which generalizes Kleinecke’s ideal of inessential operators. For certain subspaces of , it is shown that when has a generalized inverse modulo , then there exists a projection such that has a generalized inverse and .