A Note on the Sequence Space b_p^(r,s) (G)

A note on modular hyperconvex space

A note on a symplectic structure on the space of G-monopoles

a note on modular hyperconvex space

A Note on the Symplectic Structure on the Space of G-monopoles

1.1. Let G be a semisimple complex Lie group with the Cartan datum (I, ·) and the root datum (Y,X, . . . ). Let H ⊂ B = B+,B− ⊂ G be a Cartan subgroup and a pair of opposite Borel subgroups respectively. Let X = G/B be the flag manifold of G. Let C = P ∋ ∞ be the projective line. Let α = ∑ i∈I aii ∈ N[I] ⊂ H2(X,Z). The moduli space of G-monopoles of topological charge α (see e.g. [4]) is natura...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...