We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS. Thereafter, non-asymptotic high-probability bounds are established on the e...

We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing 2 dimensional perturbations of plane Couette flow. We prove estimates on the L2 norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the unstable half plane. For the remaining region, we show that...

Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T -transitivity. It will be shown that preservation of T -transitivity is closely relat...

A Banach space X has the 2-summing property if the norm of every linear operator from X to a Hilbert space is equal to the 2-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar eld: the property is self-dual and any space with the property is a nite dimensional space of maximal distance to the Hilbert space of the same dimensio...

A Banach space X has the 2-summing property if the norm of every linear operator from X to a Hilbert space is equal to the 2-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar field: the property is self-dual and any space with the property is a finite dimensional space of maximal distance to the Hilbert space of the same dime...

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...

The diamond norm plays an important role in quantum information and operator theory. Recently, it has also been proposed as a reguralizer for low-rank matrix recovery. The norm constants that bound the diamond norm in terms of the nuclear norm (also known as trace norm) are explicitly known. This note provides a simple characterization of all operators saturating the upper and the lower bound.

the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

The purpose of the present notes is to examine following issues related Chernoff estimate: (1) For contractions on a Banach space we modify $\sqrt{n}$-estimate and apply it in proof product formula for $C_0$-semigroups \textit{strong} operator topology. (2) We use idea {probabilistic} approach, proving estimate strong topology, uplift \textit{operator-norm} \textit{quasi-sectorial} contraction ...

The operator Aε = D1g1(x1/ε, x2)D1 + D2g2(x1/ε, x2)D2 is considered in L2(R ), where gj(x1, x2), j = 1, 2, are periodic in x1 with period 1, bounded and positive definite. Let function Q(x1, x2) be bounded, positive definite and periodic in x1 with period 1. Let Q(x1, x2) = Q(x1/ε, x2). The behavior of the operator (Aε + Q ) as ε → 0 is studied. It is proved that the operator (Aε +Q ) tends to ...