Abstract The Fueter-Sce-Qian mapping theorem gives a constructive way to extend holomorphic functions of one complex variable slice hyperholomorphic functions. By means the Cauchy formula for it is possible have in integral form n odd. On this based $$ \mathcal {F}$$ F -functional calculus -tuples commuting o...

A transitive (infinite) permutation group which has m orbits on ordered pairs of distinct points has at least mn−1 orbits on ordered n-tuples. This is best possible, and groups attaining the bound can be characterised.

Proof. For two commuting matrices A and B, each eigenspace of A is invariant under B. Indeed, if (A−λIn)v = 0 then (A−λIn)Bv = B(A−λIn)v = B(0) = 0. For n = 1, each element of F is a complex number; thus, the statement of the lemma is true. Suppose the statement of the lemma is true for all n < m for some m ≥ 2. Let F be a set of mutually commuting diagonalizable matrices in Mm(C). Take A ∈ F ....

We define a smooth functional calculus for a noncommuting tuple of (unbounded) operators Aj on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.

We consider a filtration of the K-theory space for a regular noetherian ring proposed by Goodwillie and Lichtenbaum and show that its successive quotients are geometric realizations of explicit simplicial abelian groups. The filtration in weight t involves t-tuples of commuting automorphisms of projective R-modules. It remains to show that the Adams operations act appropriately on the filtration.

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...

In this paper, we study skew (A,m)-symmetric operators in a complex Hilbert space H. Firstly, by introducing the generalized notion of left invertibility show that if T ? B(H) is (A,m)-symmetric, then eisT (A,m)-invertible for every s R. Moreover, examine some conditions (A,m)- symmetric to be (A,m?1)-symmetric. The connection between c0-semigroups (A,m)-isometries and (A,m)-symmetries also des...

Extension results, expressed in terms of complete boundedness, leading to necessary and sufficient conditions for the solvability of power moment problems with unbounded operator data are given. As an application, necessary and sufficient conditions for the existence of selfadjoint and normal extensions for some classes of commuting tuples of unbounded linear operators are obtained.

We study the space of all d-tuples unitaries u = ( 1 , … d ) using dilation theory and matrix ranges. Given two such v generating, respectively, C*-algebras A B, we seek minimal constant c that ≺ by which mean there exist faithful ∗-representations π : → B H ρ K with ⊆ for i, i is equal to compression P | H. This gives rise a metric D log max { } on set equivalence classes ∗-isomorphic tuples u...