In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

Abstract We study the question for which Tychonoff spaces X and locally convex E space of continuous ‐valued functions on contains a complemented copy , both endowed with pointwise topology. provide positive answer vast class spaces, extending classical theorems Cembranos, Freniche, Domański Drewnowski, proved case Banach Fréchet . Also, given infinite Y we show that if only any such subspace.

Let η be a regular cardinal. It is proved, among other things, that: (i) if J(η) is the corresponding long James space, then every closed subspace Y ⊆ J(η), with Dens(Y ) = η, has a copy of `2(η) complemented in J(η); (ii) if Y is a closed subspace of the space of continuous functions C([1, η]), with Dens(Y ) = η, then Y has a copy of c0(η) complemented in C([1, η]). In particular, every nonsep...

Two methods of constructing infinitely many isomorphically distinct Lpspaces have been published. In this article we show that these constructions yield very different spaces and in the process develop methods for dealing with these spaces from the isomorphic viewpoint. We use these methods to give a complete isomorphic classification of the spaces Rp constructed by Bourgain, Rosenthal, and Sch...

The operator spaces Hk n 1 ≤ k ≤ n, generalizing the row and column Hilbert spaces, and arising in the authors’ previous study of contractively complemented subspaces of C∗-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from Hk n to row or column space is...

We show that the classification problem for genus n Banach spaces can be reduced to the unconditionally primary case and that the critical case there is n = 2. It is further shown that a genus n Banach space is unconditionally primary if and only if it contains a complemented subspace of genus (n − 1). We begin the process of classifying the genus 2 spaces by showing they have a strong decompos...

Let |·| be the standard Euclidean norm on ℝ n and let X=(ℝ ,∥·∥) a normed space. A subspace Y⊂X is strongly α-Euclidean if there constant t such that t|y|≤∥y∥≤αt|y| for every y∈Y, say it α-complemented ∥P Y ∥≤α, where P orthogonal projection from X to ∥ denotes operator of with respect X. We give an example space arbitrarily high dimension 2-Euclidean but contains no 2-dimensional both (1+ϵ)-Eu...

A theorem of Giesy and James states that c0 is nitely representable in James' quasire exive Banach space J2. We extend this theorem to the p th quasi-re exive James space Jp for each p ∈ (1,∞). As an application, we obtain a new closed ideal of operators on Jp, namely the closure of the set of operators that factor through the complemented subspace (`∞ ⊕ `∞ ⊕ · · · ⊕ `∞ ⊕ · · · )`p of Jp. 2010 ...