We investigate the distribution of eigenvalues of completely nuclear maps on an operator space. We prove that eigenvalues of completely nuclear maps are square-summable in general and summable if the underlying operator space is Hilbertian and homogeneous. Conversely, if eigenvalues are summable for all completely nuclear maps, then every finite dimensional subspace of the underlying operator s...

We present telescoping algorithms which compute optimal sum representations of indefinite nested sums. More precisely, given a rational summand expression in terms of nested sums and products, the algorithm splits the summand into a summable part, which can be summed by telescoping, and into a non-summable part, which is degree-optimal with respect to one of the most nested sums or products. If...

Abstract Consider a topologically transitive countable Markov shift $\Sigma $ and summable locally constant potential $\phi with finite Gurevich pressure $\mathrm {Var}_1(\phi ) < \infty . We prove the existence of limit $\lim _{t \to } \mu _t$ in weak $^\star topology, where $\mu is unique equilibrium state associated to $t\phi In addition, we present examples at zero temperature exists for...

In this paper we define and study a vector-valued sequence space, called the space of anisotropic (s, q, r)-summable sequences, that generalizes classical (s; q)-mixed sequences (or mixed q)-summable sequences). Furthermore, two classes linear operators involving new one them class q) -mixed due A. Pietsch. Some characterizations, inclusion results Pietsch domination-type theorem are presented ...

In our recent paper we obtained an extension of a theorem Tam (2018), which was established for iterates set-valued paracontracting operators in finite-dimensional Euclidean space. This exact maps metric the present prove two analogs this result inexact under presence computational errors. first result, errors are summable, while second one they converge to zero. particular case Banach space, i...

and a method A of summability by means of which a given sequence Su S2, • • • is summable to <r as w—»oo. If a sequence sn is summable A, we say that A {sn} exists and that sn belongs to the summability field of A. If sn is summable A to <r, we say that A {sn} = <r. The method A is regular if A {sn} = lim sn whene...

Expansive algebraic Z-actions corresponding to ideals are characterized by the property that the complex variety of the ideal is disjoint from the multiplicative unit torus. For such actions it is known that the limit for the growth rate of periodic points exists and equals the entropy of the action. We extend this result to actions for which the complex variety intersects the multiplicative to...

This paper is a continuation of our paper [21]. We give an analogue of the necessary and sufficient condition for summable set (i.e. the main theorem of [21]) with respect to summable set by a functional L in real Hilbert space. After presenting certain useful lemmas, we prove our main theorem that the summability for an orthonormal infinite set in real Hilbert space is equivalent to its summab...

It is proved that if A is an abelian p-group with a pure subgroup G so that A/G is at most countable and G is either p-totally projective or p-summable, then A is either p-totally projective or p-summable as well. Moreover, if in addition G is nice in A, then G being either strongly p-totally projective or strongly p-summable implies that so is A. This generalizes a classical result of Wallace ...

To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose “Riemannian” aspect (Hilbert space and Dirac operator) encode the boundary action through its Patterson-Sullivan measure. We prove that the ergodic rigidity theorem for this boundary action implies that the zet...