We give a systematic study on the Hardy spaces of functions with values in the non-commutative L-spaces associated with a semifinite von Neumann algebra M. This is motivated by the works on matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), and on the other hand, by the recent development on the non-commutative martingale inequalities. Our non-com...

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case. Our general setting is that of operator-valued kernels corresponding to RKHS of functions with values in a Hilbert space. We show that in general, for a give...

In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪→ H ↪→ V ∗ with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V ∗. The system is given by dx+A(dt, x) = f(t, x)γ(dt) +B(t)u(dt), x(0...

The notion of operator-valued frames (OVFs) by Kaftal et al. (Trans Am Math Soc 361(12):6349–6385, 2009) and G-frames Sun (J Anal Appl 322(1):437–452, 2006) do not include all generalizations notions for Hilbert spaces. For this purpose, we introduce the weak (weak OVFs) which covers known Theory weak-OVFs is more demanding than theory OVFs due to following: One, frame operator may factor anoth...

We study a new system of nonlinear set-valued variational inclusions involving a finite family of H ·, · -accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of H ·, · -accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme...

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...

In this paper, a new system of nonlinear set-valued variational inclusions involving (H, η)-monotone mappings in Hilbert spaces is introduced and studied. By using the resolvent operator method associated with (H, η)-monotone mappings, an existence theorem of solutions for this kind of system of nonlinear set-valued variational inclusion is established and a new iterative algorithm is suggested...