Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.
A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.
The Mazur-Ulam theorem [15] has been formulated as two registrations: cluster bijective isometric -> midpoints-preserving Function of E, F; and cluster isometric midpoints-preserving -> Affine Function of E, F; A proof given by Jussi Väisälä [23] has been formalized.
We prove, among other things, that the space C[0,ω₂] has no countably norming Markushevich basis. This answers a question asked by G. Alexandrov and A. Plichko.
This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai’s generalize central approximate identities in ideals in C*-algebras, for it is proved that if X admits an M-cai in Y, then X is a complete M-ideal in Y. It is proved, using ’special’ M-cai’s, that if J is a nuclear ideal in a C*-algebra A, then J is completely complemented in Y for any (isomorphically) locally reflexive operator space Y with J ⊂ Y ⊂ A and...
Let be a locally compact abelian group and be the space of bounded convolution...
We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.