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...

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum t...

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T (·), where p ∈ X and S and T are maximal monotone operators on the reflexive Banach space X . The...

We introduce composite iterative schemes by the viscosity iteration method for finding a zero of an accretive operator in reflexive Banach spaces. Then, under certain differen control conditions, we establish strong convergence theorems on the composite iterative schemes. The main theorems improve and develop the recent corresponding results of Aoyama et al. 2007 , Chen and Zhu 2006, 2008 , Jun...

The objective of this paper is to introduce a general scheme for deriving a posteriori error estimates by using duality theory of the calculus of variations. We consider variational problems of the form inf v∈V {F (v) +G(Λv)}, where F : V → R is a convex lower semicontinuous functional, G : Y → R is a uniformly convex functional, V and Y are reflexive Banach spaces, and Λ : V → Y is a bounded l...

This paper introduces a novel monotonic modal logic, allowing us to capture the nonmonotonic variant of the modal logic S4F: we add a second new modal operator into the original language of S4F, and show that the resulting formalism is strong enough to characterise the logical consequence of (nonmonotonic) S4F, as well as its minimal model semantics. The latter underlies major forms of nonmonot...

On a reflexive Banach space X , if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum σ(T ) ⊆ R, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can constru...

Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y , respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is defined by σπ(A) = {z ∈ σ(A) : |z| = maxw∈σ(A) |w|}, where σ(A) denotes the spectrum of A. Assume that Φ : A → B is a map and the range of Φ contains all operators with rank at most two. It is pr...

Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for Banach spaces involving a cylindrical Wiener process as integrator and an operator-valued stochastic process as integrand is defined. Basic properties of this integral are stated and proved. A class o...