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...

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 develop a natural generalization of vector-valued frame theory, which we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointedness, compl...

Operations with tensors, or multiway arrays, have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-1 outer products using either the CANDECOMP/PARAFAC (CP) or the Tucker models, or some variation thereof. Such decompositions are motivated by specific applications where the goal is to find an approximate such representation for ...

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-m...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...