This paper considers when one can invert general recursive operators which map a class of functions F to F . In this regard, we study four different notions of inversion. We additionally consider enumeration of operators which cover all general recursive operators which map F to F in the sense that for every general recursive operator Ψ mapping F to F , there is a general recursive operator in ...

(b) We know that T is invertible if and only if its matrix is invertible with respect to any basis; we also know that a matrix is invertible if and only if its determinant is zero. If A is a matrix representing T in some basis, then T is invertible if and only if A is invertible if and only if det(T ) = det(A) 6= 0. (c) If T has matrix A under some basis, then T−1 has matrix A−1 under the same ...

Using ideas of S. Wassermann on non-exact C∗-algebras and property T groups, we show that one of his examples of non-invertible C∗-extensions is not semiinvertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a C∗-extension which is not even invertible up to homotopy. Introduction The Brown–Dougla...

For a locally compact abelian group $G$, J. L. Taylor (1971) gave complete characterization of invertible elements in the measure algebra $M(G)$. Using Fourier-Stieltjes transform, this can be carried out context algebras $B(G)$. We obtain latter for $B(G)$ certain classes groups, particular, many totally minimal groups and $ax+b$-group.

Stabilization problems of linear systems with right invertible constraints have mostly been solved for both global and semi-global frameworks. Linear systems subject to non-right invertible constraints have completely different characteristics compared to those with right invertible constraints. This paper addresses the control problems of linear systems subject to non-right invertible constrai...

We give an explicit description of $$\overline{{\mathcal {M}}}_{1,2}$$ as a weighted blow-up projective stack. use this to compute the Brauer group {M}}}_{1,2;S}$$ over any base scheme S where 6 is invertible, and integral Chow rings $${\mathcal {M}}_{1,2}$$ .

Let R be an associative ring with 1 and R the multiplicative group of invertible elements of R. In the paper, subgroups of R which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the cor...

We show that if T is an isometry (as metric spaces) from an open subgroup of the invertible group A of a unital Banach algebra A onto an open subgroup of the invertible group B of a unital Banach algebra B, then T is extended to a real-linear isometry up to translation between these Banach algebras. We consider multiplicativity or unti-multiplicativity of the isometry. Note that a unital linear...

In this paper, we study algorithmic problems for automaton semigroups and automaton groups related to freeness and finiteness. In the course of this study, we also exhibit some connections between the algebraic structure of automaton (semi)groups and their dynamics on the boundary. First, we show that it is undecidable to check whether the group generated by a given invertible automaton has a p...