For a locally compact group G and p ∈ (1,∞), we define Bp(G) to be the space of all coefficient functions of isometric representations of G on quotients of subspaces of Lp spaces. For p = 2, this is the usual Fourier–Stieltjes algebra. We show that Bp(G) is a commutative Banach algebra that contractively (isometrically, if G is amenable) contains the Figà-Talamanca–Herz algebra Ap(G). If 2 ≤ q ...

In this note we include two remarks about bounded (not necessarily contractive) linear projections on a von Neumann-algebra. We show that if M is a von Neumann-subalgebra of B(H) which is complemented in B(H) and isomorphic to M ⊗ M then M is injective (or equivalently M is contractively complemented). We do not know how to get rid of the second assumption on M. In the second part,we show that ...

A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of `p-strictly singular operators, and we also investigate the structure of general `p-strictly singular operators on Lp. The main result is that if an operator T on Lp, 1 < p < 2, is `p-strictly singular ...

In this article we deal with the free Banach lattice generated by a and its behavior respect to subspaces. general, any embedding $i\colon \mathbb{L} \longrightarrow \mathbb{M}$ between two lattices $\mathbb{L} \subseteq induces homomorphism $\hat \imath\colon FBL \langle \rangle \mathbb{M}\rangle$ corresponding lattices. We show that mapping \imath$ might not be an isometric neither isomorphic...

A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of `p-strictly singular operators, and we also investigate the structure of general `p-strictly singular operators on Lp . The main result is that if an operator T on Lp , 1 < p < 2, is `p-strictly singula...

We present new constructions for (n, w, λ) optical orthogonal codes (OOC) using techniques from finite projective geometry. In one case codewords correspond to (q − 1)-arcs contained in Baer subspaces (and, in general, kth-root subspaces) of a projective space. In the other construction, we use sublines isomorphic to PG(1, q) lying in a projective plane isomorphic to PG(1, qk), k > 1. Our const...

A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if E0 does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace ...

A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic nature which implies an interesting dichotomy for subspaces of Banach spaces. Combined with a result of Komorowski and TomczakJaegermann, this gives a positive...

It is well known that the set of all ideals(2) of a ring forms a complete modular lattice with respect to set inclusion. The same is true of the set of all right ideals. Our purpose in this paper is to consider the consequences of imposing certain additional restrictions on these ideal lattices. In particular, we discuss the case in which one or both of these lattices is complemented, and the c...