Each infinitesimally faithful representation of a reductive complex connected algebraic group G induces a dominant morphism Φ from the group to its Lie algebra g by orthogonal projection in the endomorphism ring of the representation space. The map Φ identifies the field Q(G) of rational functions on G with an algebraic extension of the field Q(g) of rational functions on g. For the spin repres...

In this paper we consider a completely positive map τ = (τ t , t ≥ 0) with a faithful normal invariant state φ on a type-II 1 factor A 0 and propose an index theory. We achieve this via a more general Kolmogorov's type of construction for stationary Markov processes which naturally associate a nested isomorphic von-Neumann algebras. In particular this construction generalizes well known Jones c...

and Applied Analysis 3 R1 F T / ∅; R2 φ p, Tx ≤ φ p, x , for all x ∈ C, p ∈ F T ; R3 F T F̂ T . Definition 1.4. A point p ∈ C is said to be an strong asymptotic fixed point of T if C contains a sequence {xn}n 0 which converges strongly to p and limn→∞‖xn − Txn‖ 0. The set of strong asymptotic fixed points of T is denoted by F̃ T . We say that a mapping T is weak relatively nonexpansive see, e.g.,...

<p>The conceptions of <em>b</em>-metric spaces and metric play a remarkable role in proving many theorems uniqueness existence solution such equations as integral or differential equations. The conception extended is considered generalization concept this was employed to unify some new fixed point results the literature. On other hand, simulation functions founded 2020 name ℋ-...

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if φ : M → N is a horizontally conformal map such that the tension field is divergence free, then φ is harmonic. Furthermore, if N is noncompact, then φ must be constant. Also we show that the projection of a warped product manifold onto the first component is harmonic...

We build a new estimate relative with Hermite functions based upon oscillatory integrals and Langer's turning point theory. From it we show that the equationi∂tu=−∂x2u+x2u+ϵ〈x〉μW(νx,ωt)u,u=u(t,x),x∈R,0≤μ<13, can be reduced in H1(R) to an autonomous system for most values of frequency vector ω ν, where W(φ,θ) is smooth map from Td×Tn R odd φ.

We prove the termination of 4-fold canonical flips. This paper is a supplement of [KMM, Theorem 5-1-15] and [M, Main Theorem 2.1]. We prove that a sequence of 4-fold log flips for canonical pairs terminates after finitely many steps. Let us recall the definition of canonical flips, which is slightly different from the usual one (cf. [S, (2.11) Adjoint Diagram]). Definition 1 (Canonical flip). L...

Let (X,S) and (Y, T ) be topological dynamical systems and π : X → Y a factor map. A function F ∈ C(X) is a compensation function for π if P (F + φ ◦ π) = P (φ) for all φ ∈ C(Y ). For a factor code between subshifts of finite type, we analyze the associated relative entropy function and give a necessary condition for the existence of saturated compensation functions. Necessary and sufficient co...