The vertex operators Hm act on the Hall-Littlewood polynomials HX; t] with the property that HmHX; t] = H (m;;) X; t]. We present a combinatorial rule for computing the action of Hm on the schur function basis which interpolates the Pieri formula for multiplication by hmX] and the schur function vertex operator. This rule suggests the existence of an operator on column strict tableaux of conten...

This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai's generalize central approximate identities in ideals in C *-algebras, for it is proved that if X admits an M-cai in Y , then X is a complete M-ideal in Y. It is proved, using " special " M-cai's, that if J is a nuclear ideal in a C *-algebra A, then J is ...

Let $M$ and $N$ be Archimedean vector lattices. We introduce orthogonally additive band operators inverse from to examine their properties. investigate the relationship between disjointness preserving show that under some assumptions on lattices or $N$, these two classes are same. By using this relation, we if ${\mu }$ is a bijective operator (resp. operator) into then }^{-1}$:$N$${\rightarrow}...

Let (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) be a contractive iterated function system (IFS), where X is a compact subset of R. It is well known that there exists a unique nonempty compact set K such that K = ⋃m j=1 wj(K). Moreover, the Ruelle operator on C(K) determined by the IFS (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) has been introduced in [FL]. In the present paper, the Ruelle operators det...

Common ground to the three concepts are special polynomial sequences, called She er sequences. A polynomial sequence (sm (x))m2N0 is a sequence of polynomials sm (x) 2 K [x] such that deg sm = m, s0 6= 0. It is convenient to de ne sm = 0 for negative m. The coe cient ring K is assumed to be an integral domain. For this introduction to Finite Operator Calculus it su ces to choose K as R [!], the...

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...

Let X be a locally compact Hausdorff space with n proper continuous self maps τ i : X → X for 1 ≤ i ≤ n. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra A(X, τ) and the semicrossed product C 0 (X) × τ F + n. We introduce a concept of conjugacy for multidimensional systems , which we coin p...

We show that the existence of a nontrivial bounded uniformly continuous (BUC) complete trajectory for a C0-semigroup TA(t) generated by an operator A in a Banach space X is equivalent to the existence of a solution Π = δ0 to the homogenous operator equation ΠS|M = AΠ. Here S|M generates the shift C0-group TS(t)|M in a closed translation-invariant subspaceM of BUC(R, X), and δ0 is the point eval...