In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.

We prove the GSS conjecture of Garcia, Stillman and Sturmfels, which states that the ideal of the variety of secant lines to a Segre product of projective spaces is generated by 3 × 3 minors of flattenings. We also describe the decomposition of the coordinate ring of this variety as a sum of irreducible representations.

In this paper we use the concept of wavelet sets, as introduced by X. Dai and D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary n×n integer dilation matrix as a direct integral of irreducible monomial representations. In so doing we generalize a result of F. Martin and A. Valette in which they show that the wavelet representation is weakly equiv...

In this paper we use the concept of wavelet sets as introduced by X. Dai and D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary n×n integer dilation matrix as a direct integral of irreducible monomial representations. In so doing we generalize a result of F. Martin and A. Valette in which they show that the wavelet representation is weakly equiva...

We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be described by the combination of two different types of maps. We also show that a rank preserving map can be implemented by only one type if the corresponding lat...

In this paper, we have proposed some new upper bounds for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor, which improve the known upper bounds obtained in Chang et al. (Linear Algebra Appl 438:4166-4182, 2013), Song and Qi (SIAM J Matrix Anal Appl 34:1581-1595, 2013), He and Huang (Appl Math Lett 38:110-114, 2014), Li et al. (J Comput Anal Appl 483:182-199, 2...

We pose a conjecture for the expected number of generators of the ideal of the union C of s general rational irreducible curves in P r. By using the computer we prove the conjecture for C of low degree d (e.g. if s = 1 for d 80 and if s 10 for d 40).

Given a right ideal I in ring R, the idealizer of R is largest subring which becomes two-sided ideal. In this paper we consider idealizers second Weyl algebra A2, differential operators on k[x,y] (in characteristic 0). Specifically, let f be polynomial x and y defines an irreducible curve whose singularities are all cusps. We show that fA2 A2 always left noetherian, extending work McCaffrey.

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

Let [Formula: see text] be a commutative ring with text]. We introduce the concept of weakly 1-absorbing primary ideal, which is generalization ideal. A proper ideal said to if whenever nonunit elements and text], we have or number results concerning ideals are given, as well examples ideals. Furthermore, give corrected version result on rings.