we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

where we used the fact that (σ 2 z) = 1 . In general e−iφfn·fσ = 1 cos(φ)− in · nσ sin(φ) Now we consider a system composed of two subsystems H = H1 ⊗H2, each being a two-level system. To describe operators on the two subsystems we normally use the shorthanded notations A ≡ A ⊗ 1 2 and B ≡ 1 1 ⊗B2 and AB ≡ A ⊗B2 . a) What is (σσ) z z ? b) Consider the operator U = e− 1 iσ iσ φ⊗ z e− z : to whic...

and Applied Analysis 3 nonexpansive mapping such that F S ∩ A−10/ ∅. Let {xn} be a sequence generated by x0 x ∈ C and un J−1 ( βnJxn ( 1 − βn ) JSJrnxn ) , Cn { z ∈ C : φ z, un ≤ φ z, xn } , Qn {z ∈ C : 〈xn − z, Jx0 − Jxn〉 ≥ 0}, xn 1 ΠCn∩Qnx0 1.6 for all n ∈ N ∪ {0}, where J is the duality mapping on E, {βn} ⊂ 0, 1 , and {rn} ⊂ a,∞ for some a > 0. If lim infn→∞ 1 − βn > 0, then {xn} converges s...

‎in this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by zou [operator inequalities associated with tsallis relative operator entropy‎, ‎{em math‎. ‎inequal‎. ‎appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and tsallis relative o...

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted po...

We prove the following statements about bounded linear operators on a separable, complex Hilbert space: (1) Every normal operator N that is similar to a Hilbert-Schmidt perturbation of a diagonal operator D is unitarily equivalent to a Hilbert-Schmidt perturbation of D; (2) For every normal operator A', diagonal operator D and bounded operator X, the Hilbert-Schmidt norms (finite or infinite) o...

We show that universality arguments, namely the Svetitsky–Yaffe conjecture, allow one to obtain exact results on the critical behavior of 3D SU(2) gauge theory at the finite temperature deconfinement transition, through a mapping into the 2D Ising model. In particular, we consider the finite–size scaling behavior of the plaquette operator, which can be mapped into the energy operator of the 2D ...

Let E and P be nonnegative quadratic forms in a Hilbert space H and assume that E + bP is densely defined and closed for every b ≥ 0. For every b > 0 let Hb be the self-adjoint operator associated with E + bP in the sense of Kato’s representation theorem. By Kato’s monotone convergence theorem, the operators (Hb + 1) −1 converge strongly to an operator L, as b tends to infinity. Let k ∈ N. We g...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

Let E and F be Banach lattices and assume E∗ has no atoms. Let T : E → F be a norm bounded disjointness preserving operator from E into F . Then β(T ) = α(T ) = ‖T‖e = ‖T‖.