Let be a regular cardinal. It is proved, among other things, that: (i) if J() is the corresponding long James space, then every closed subspace Y J(), with Dens(Y) = , has a copy of`2 () complemented in J(); (ii) if Y is a closed subspace of the space of continuous functions C((1; ]), with Dens(Y) = , then Y has a copy of c 0 () complemented in C((1; ]). In particular, every nonseparable closed...

In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the bounded compact approximation property, then L∞/X has the bounded compact approximation property. We also show that X∗ has the λ-BCAP with conjugate operators if and only if the pair (X,Y ) has the λ-BCAP for each...

Rosenthal [R] introduced the Lp space Xp in 1971. Among its interesting properties are that it contains and is contained in isomorphs of lp ⊕ l2, but is not isomorphic to a complemented subspace of lp⊕ l2. These properties have made Xp rather resistant to standard approaches to classifying its complemented subspaces. For example it was first proved that Xp was primary in [JO2] where the device ...

This paper deals with certain properties of the subspaces of LC(H) and C and namely those connected with the reflexivity and with the property of containing classical spaces. It is proved that any subspace of C (1 < p < oo) is either isomorphic to Hilbert space or it contains a subspace isomorphic to I . For Cj and LC'H) the same results were obtained by J. R. Holub, cf. [4]. Introduction. Let ...

It is shown that the invariant subspace of the Bergman space Ap of the unit disc, generated by a finite union of Hardy interpolation sequences, is complemented in Ap. Let D be the open unit disc of the complex plane C, and let H = H(D) denote the usual Hardy space. For 0 < p < ∞ the Bergman space A consists of analytic functions f on D such that ‖f‖p = ∫ D |f(z)| dA(z) < ∞, where dA is area mea...

It is proved that the Disc Algebra does not contain a complemented subspace isomorphic to the space C(k)(Td) of k times continuously differentiable functions on the d-dimensional torus ( k = 1, 2, ... ; d = 2, 3, ... ). Introduction. Recall two interesting problems concerning the space q 1)(T2 ) of continuously differentiable functions on the 2-dimensional torus T2 . (I) Is C(1)(T2 ) isomorphic...

Abstract. It is shown that for an L1-predual space X and a countable linearly independent subset of ext(BX∗) whose norm-closed linear span Y in X∗ is w∗-closed, there exists a w∗-continuous contractive projection from X∗ onto Y . This result combined with those of Pelczynski and Bourgain yields a simple proof of the Lazar-Lindenstrauss theorem that every separable L1-predual with non-separable ...

An important problem in topology is to determine the effects on the function space of imposing some natural topological condition on the space X [5]. In this way, it is practical to characterize the complemented subalgebras of Banach algebras. In our investigation, we relate the second category property of [0,1] with certain properties of the complemented subalgebras of bounded real Baire-1 fun...