We study the question of whether or not contractive representations of logmodular algebras are completely contractive. We prove that a 2-contractive representation of a logmodular algebra extends to a positive map on the enveloping C∗-algebra, which we show generalizes a result of Foias and Suciu on uniform logmodular algebras. Our proof uses non-commutative operator space generalizations of cl...

The almost Mathieu operator is the discrete Schrodinger Hα,β,θ on \(\ell ^2(\mathbb {Z})\) defined via \((H_{\alpha ,\beta ,\theta }f)(k) = f(k + 1) - \beta \cos {}(2\pi \alpha k \theta ) f(k)\). We derive explicit estimates for eigenvalues at edge of spectrum finite-dimensional \({H^{(n)}_{\alpha }}\). furthermore show that (properly rescaled) m-th Hermite function ϕm an approximate eigenvecto...

Patients with chronic pain due to neuropathy or musculoskeletal injury frequently exhibit reduced alpha and increased theta power densities. However, little is known about electrical brain activity and chronic pain in patients with rheumatoid arthritis (RA). For this purpose, we evaluated power densities of spontaneous electroencephalogram (EEG) band frequencies (delta, theta, alpha, and beta) ...

In order to solve domain equations over 1-bounded compact metric spaces, xed points of functors on categories of 1-bounded compact metric spaces are studied. Two categories of 1-bounded compact metric spaces are considered: KMS and KMS E. In both categories, objects are isomorphic if and only if they are isometric. As a consequence, provided that the operation of a domain equation can be extend...

In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the ”strange” function F (q) of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan’s mock theta functions. Using these functions and their transformation behaviour, we also compute asymptotic expansions similar to expansions of F (q).

we provide fuzzy quasi-metric versions of a fixed point theorem ofgregori and sapena for fuzzy contractive mappings in g-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.

We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.

Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F S ∩ F T / ∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as xn 1 βnxn 1 − βn Syn, yn αnγ...