The Cayley-Dickson loop Cn is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley-Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, sedenions). We will discuss properties of the Cayley-Dickson loops, show that these loops are Hamiltonian and describe the structure of th...

Operator stable laws are the limits of operator normed and centered sums of independent, identically distributed random vectors. The operator ν-stable laws are the analogous limit distributions for randomized sums. In this paper we characterize operator ν-stable laws and their domains of attraction. We also discuss several applications, including the scaling limits of continuous time random wal...

Harmonic Analysis [59] N. Bourbaki. Théories spectrales, Chapitres 1 et 2. Éléments de Mathématique,Réimpression inchangée de l’édition originale de 1967, Springer-Verlag, 2007[60] G. B. Folland. A Course in Abstract Harmonic Analysis. CRC Press, 1995[61] L. H. Loomis. An Introduction to Abstract Harmonic Analysis. van Nostrand,1953[62] M. A. Năımark. Normed Algebras. Third ...

Cosine Numeric Abstract, Cosine Logical Abstract, Overlap Logical Overlap Logical Abstract, Cosine Numeric Cosine Numeric Text, Cosine Numeric Text, Cosine Logical Text, Overlap Logical Abstract, Cosine Numeric Cosine Numeric Abstract, Cosine Logical Cosine Logical Title, Cosine Numeric EVALUATION MEASURE Normed. Recall Normed. Precision Normed. Recall Normed. Precision Normed. Recall Normed. P...

Several kinds of quotient triangulated categories arising naturally in representations of algebras are studied; their relations with the stable categories of Frobenius exact categories are investigated; the derived categories of Gorenstein algebras are explicitly computed inside the stable categories of the graded module categories of the corresponding trivial extension algebras; new descriptio...

The Jiang–Su algebra Z has come to prominence in the classification program for nuclear C-algebras of late, due primarily to the fact that Elliott’s classification conjecture predicts that all simple, separable, and nuclear C-algebras with unperforated K-theory will absorb Z tensorially (i.e., will be Z-stable). There exist counterexamples which suggest that the conjecture will only hold for si...

The aim of this paper is to continue the study of properties of an -stable at a point vector function. We show that any -stable at a point function from arbitrary normed linear space is strictly differentiable at the considered point.

Every continuous linear functional defined on a vector subspace of a real normed space can be extended to the whole space so as to remain linear and continuous, and with the same norm(2). The extension of continuous linear transformations between two real normed spaces has been studied by several authors and for a long time it has been recognized that this problem has a close connection with th...