In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them. We can also give a new estimation for the norms of a r-circulant matrix involv...

Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of focusing on the norms themselves, we study associated dual norms and dual functions. Combining this study with a variant of the Szemerédi Regularity Lemma, we give...

The algebra B of bicomplex numbers is viewed as a complexification the Archimedean f-algebra hyperbolic D. This lattice-theoretic approach allows us to establish new properties so-called D-norms. In particular, we show that D-norms generate same topology in B. We develop D-trigonometric form number which leads geometric interpretation nth roots terms polyhedral tori. use concepts developed, par...

We study a rational version of the double affine Hecke algebra associated to the nonreduced affine root system of type (C n , Cn). A certain representation in terms of differencereflection operators naturally leads to the definition of nonsymmetric versions of the multivariable Wilson polynomials. Using the degenerate Hecke algebra we derive several properties, such as orthogonality relations a...

Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference (“Dunkl”) operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth’s (arχiv:0707.0251) results for the ...

The present paper is devoted to infinite order decompositions of C*-algebras. It is proved that an infinite order decomposition (IOD) of a C*-algebra forms the complexification of an order unit space, and, if the C*-algebra is monotone complete (not necessarily weakly closed) then its IOD is also monotone complete ordered vector space. Also it is established that an IOD of a C*-algebra is a C*-...

Throughout this paper A will denote a finite-dimensional associative complex algebra. A vector space norm · on A is said to be stable if there exists a positive constant σ satisfying x ≤ σ x n for every x in A and all natural numbers n. It is well known that stable norms · on A are spectrally dominant (that is, for every x in A, the inequality ρ x ≤ x holds, where ρ · denotes the spectral radiu...

We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic estimates, which show that these matrices are expected to be very well conditioned. Our probabilistic estimates for the norms of standard Gaussian random Toeplit...

One source of trust for physical trading systems is their physical assets and simply their presence. A similar baseline does not exist for electronic trading systems, but one way in which it may be possible to create that initial trust is through the abstract notion of an institution, defined in terms of norms [19] and the scenes within which (software) agents may play roles in different tradin...