We show that the numerical index of any operator ideal is less than or equal to minimum indices domain space and range space. Further, we compact operators weakly dual space, this result provides interesting examples. also a projective injective tensor product Banach spaces factors. Finally, if two has Daugavet property unit ball one factor slicely countably determined its contains point Fréche...

The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bézier curve or patch. In particular, we establish a generalization of Birch’s Theorem and use it to deduce sufficient conditions on the control points for a patch to be injective. We also explain a way that the control points influence the shape via degenerations to regu...

A tensor product surface $\mathscr {S}$ is an algebraic that defined as the closure of image a rational map $\phi$ from $\mathbb {P}^1\times \mathbb {P}^1$ to {P}^3$. We provide new determinantal representations under assumptions generically injective and its base points are finitely many locally complete intersections. These matrices built coefficients linear relations (syzygies) quadratic bih...

1. Modules: 4/2/13 1 2. Quotient Modules: 4/4/13 3 3. The Isomorphism Theorems: 4/9/13 5 4. Universal Properties: 4/11/13 7 5. The Tensor Product: 4/16/13 10 6. More Tensor Products: 4/18/13 12 7. Exact Sequences: 4/23/13 14 8. Projective and Injective Modules: 4/25/13 17 9. Finitely Generated Modules Over a Euclidean Domain: 4/30/13 19 10. Finitely Generated Modules Over a PID: 5/2/13 21 11. T...

the ordinary tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in eachcomponent. keeping this in mind, linton and banaschewski with nelson defined and studied the tensor product in an equational category and in a general (concrete) category k, respectively, using bimorphisms, that is, defined via the hom-functor on k. also, the so-called sesquilinear, or on...

In this paper, we generalize Izumi’s result on uniqueness of realization of finite C-tensor categories in the endomorphism category of the injective factor of type III1 for finitely generated strongly amenable C -tensor categories by applying Popa’s classification theorem of strongly amenable subfactors of type III1.