The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this generic problem in a Hilbert space setting. New primal...

The semi-topological nature of the eta-invariant of a self-adjoint elliptic differential operator derives from a relative identification with a Chern character. This remarkable semi-locality property of the eta-invariant can be seen in spectral flow formulae and many other applications [APS2, APS3, BC1, DZ1, L1]. In this paper we prove two geometric index theorems for a family of first-order el...

We introduce and study a new system of nonlinear variational-like inclusions involving sG, η maximal monotone operators, strongly monotone operators, η-strongly monotone operators, relaxed monotone operators, cocoercive operators, λ, ξ -relaxed cocoercive operators, ζ, φ, g-relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique ...

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

We introduce the notion of operator-valued infinitesimal (OVI) independence for Boolean and monotone cases. Then show that OVI (resp. monotone) is equivalent to over an algebra $2\times 2$ upper triangular matrices. Moreover, we derive formulas obtain additive convolution by reducing it case. also define cumulants study its basic properties. each independence, construct corresponding Central Li...