Related papers: Non-commutativity of exponential spectrum

We define $G$-cospectrality of two $G$-gain graphs $(\Gamma,\psi)$ and $(\Gamma',\psi')$, proving that it is a switching isomorphism invariant. When $G$ is a finite group, we prove that $G$-cospectrality is equivalent to cospectrality with…

This paper considers strongly continuous semigroups of operators on Banach lattices which are locally eventually positive, a property that was first investigated in the context of concrete fourth-order evolution equations. We construct a…

It is shown that if $A$ is a unital commutative Banach algebra with a dense set of invertible elements, then the maximal ideal space of $A$ contains no compact, locally connected, simply coconnected subspace of topological dimension $\geq…

Let A be an idempotent algebra on a 3-element domain D that omits a G-set for a factor. Suppose A is not \alpha\beta-projective (for some alpha, beta subsets of D) and is not collapsible. It follows that A is switchable. We prove that, for…

Based on his claims in 1990, Rosenberg conjectured in 1997 that the negative algebraic $K$-groups of C*-algebras are invariant under continuous homotopy. Contrary to his expectation, we prove that such invariance holds for $K_{-1}$ of…

In this article we extend our previous results for the orthogonal group, $SO(2,4)$, to its homomorphic group $SU(2,2)$. Here we present a closed, finite formula for the exponential of a $4\times 4$ traceless matrix, which can be viewed as…

Given a positive, irreducible and bounded C_0-semigroup on a Banach lattice with order continuous norm, we prove that the peripheral point spectrum of its generator is trivial whenever one of its operators dominates a non-trivial compact or…

We prove that the set of all orders of finite algebras in the groupoid variety of anti-rectangular Abel Grassmann bands consists of all powers of four. We also prove that any groupoid anti-isomorphic to a finite or countable…

For $n\geq 2$, the homotopy groups $\pi_n(S^2)$ are non-zero.

We prove that finite-spectrum representations of compact quantum groups either in unital $C^*$-algebras $A$ or on Banach spaces $E$ exhibit the same Banach-space-modeled differential-geometric structure as their classical analogues: (a)…

We prove the Gap Theorem for the spectrum of topological modular forms $\mathrm{Tmf}$. This removes a longstanding circularity in the literature, thereby confirming the computation of $\pi_\ast \mathrm{tmf}$ from over two decades ago by…

We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds $L^\infty$ and the transformation fails to be Markov. Constructing a family…

Let $\mathcal A$ be a semisimple commutative Banach algebra. It is shown that either $\mathcal A$ has exactly one uniform norm or it admits uncountably many uniform norms. Further, it is shown that there always exists a largest closed…

In this paper we consider PI-algebras $A$ over $\R$ or $\C$. It is well known that in general such algebras are not normed algebras. In fact, there is a nilpontent commutative algebra which is not a normed algebra, see [1]. Here we address…

We show that certain dense and spectral invariant subalgebras of a $C^*$-algebra have the same bilateral Bass stable rank. This is a partial answer for (a version of) an open problem raised by R.G. Swan. Then, for certain Banach algebras,…

Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the $L^p_{\omega}-$conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the…

We present a general method to obtain a closed, finite formula for the exponential map from the Lie algebra to the Lie group, for the defining representation of the orthogonal groups. Our method is based on the Hamilton-Cayley theorem and…

Suppose that $\{\lambda_n\}_{n=1}^{\infty}$ is a sequence of distinct positive real numbers satisfying the conditions inf$\{\lambda_{n+1}-\lambda_n \}>0,$ and $\sum_{n=1}^{\infty}\lambda_n^{-1}<\infty.$ We prove that the exponential system…

Let $A$ be a non-unital Banach algebra and let $A_e = A \oplus {\mathbb C}1$ be the unitization of $A$. It is true that if $A_e$ has the spectral extension property (SEP), then $A$ has the same. Does the converse hold? In this paper, we…

In the following we are interested in the spectral gaps of discrete quasiperiodic Schr\"odinger operators when the frequency is Diophantine, the potential is analytic, and in the subcritical regime. The gap-labelling theorem asserts in this…