Let T be a CQ(N) contraction on a separable Hubert space and let / — S(qPi) ffi S(<p¿) © • • ■ ®5(qpt) be its Jordan model, where m„ qpj,.. ., <pk are inner functions satisfying <ty|m,_i for j = 2, 3,..., k, and S(<fj) denotes the compression of the shift on H2 Q <PjH2,j 1, 2,..., k. In this note we show that T is reflexive if and only if S^/ipi) is. In this note we only consider bounded linear...

Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti : K → E, i = 1, . . . ,r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed poin...

The present paper focuses on the Mandarin Intransitive keflexive Verbs. These verbs, such as zi-sha 'to commit suicide', and zi fen 'to burn oneself, are formed with a reflexive morpheme zi-'self' and a root verb. Take the verb zi-sha 'to commit suicide' for example, the reflexive morpheme contributes the reflexive meaning and the root verb sha 'to kill' contributes the meaning`to kill'; hence,...

We provide the first proof complexity results for QBF dependency calculi. By showing that the reflexive resolution path dependency scheme admits exponentially shorter Q-resolution proofs on a known family of instances, we answer a question first posed by Slivovsky and Szeider in 2014 [30]. Further, we conceive a method of QBF solving in which dependency recomputation is utilised as a form of in...

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient...