We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of the continuous section space of a Banach bundle determines completely its bundle structures. We also describe the structure of an into isometry from a continuous section space into an other. However, we demonstrate by an example that a non-surjective linear isometry can be far away from a subbundle embedding.

For Banach lattices X and Y, let X | | Y and X | | Y denote the positive projective and injective tensor products of X and Y, respectively. In this paper, we characterize the inheritance of reflexivity and containment of copies of c 0, 1, by X | | Y and X | | Y from X and Y, when one of them is an atomic Banach lattice. In this case, we also give an affirmative answer to an open question of Jeurnink.

Recently, Kawasaki and Takahashi (J. Nonlinear Convex Anal. 14:71-87, 2013) defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings (Kocourek <i>et al.</i> in Taiwan. J.Math. 14:2497-2511, 2010) and strict pseudo-contractive mappings (Browder and Petryshyn in J. Math. Anal. Appl. 20:197-228, 1967). They proved fixed point theorems for such mappings. In this paper, we prove fixed point theorems for widely more generalized hybrid non-self mappings in a Hilbert space by using the idea of Hojo <i>et al.</i> (Fixed Point Theory 12:113-126, 2011) and Kawasaki and Takahashi fixed point theorems (J.Nonlinear Convex Anal. 14:71-87, 2013). Using these fixed point theorems for non-self mappings, we proved the Browder and Petryshyn fixed point theorem (J.Math. Anal. Appl. 20:197-228, 1967) for strict pseudo-contractive

The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has a similar Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce the classes of Bregman nonspreading mappings and investigate the Mann and Ishikawa iterations for these mappings. We establish weak and strong convergence theorems for Bregman nonspreading mappings.

This paper discusses two common techniques in functional analysis: the topological method and the bornological method. In terms of Pietsch's operator ideals, we establish the equivalence of the notions of operators, topologies and bornologies. The approaches in the study of locally convex spaces of Grothendieck (via Banach space operators), Randtke (via continuous seminorms) and Hogbe-Nlend (via convex bounded sets) are compared.