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We present a reflexive Banach space $\mathfrak{X}_{_{^\text{usm}}}$ which is Hereditarily Indecomposable and satisfies the following properties. In every subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}...
Structure for Regular Inclusions     C*-diagonal  inclusions of C*-algebras  groupoid C*-algebra       font style='font-size:12px;'> 2012/3/1
We study pairs (C,D) of unital C*-algebras where D is an abelian C*-subalgebra of C which is regular in C. When D is a MASA in C, there exists a unique completely positive unital map E of C into the i...
Abstract: For a linear operator $T$ in a Banach space let $\sigma_p(T)$ denote the point spectrum of $T$, $\sigma_{p[n]}(T)$ for finite $n > 0$ be the set of all $\lambda \in \sigma_p(T)$ such that $\...
It is shown that variants of the HI methods could yield objects closely connected to the classical Banach spaces. Thus we present a new c0 saturated space, denoted as X0,with rather tight structure.
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.
Subspace structure of some operator and Banach spaces      Subspace structure  operator  Banach spaces        font style='font-size:12px;'> 2010/12/8
We construct a family of separable Hilbertian opera-tor spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete K. We also investigate ...
L- and M-structure in lush spaces      L- and M-structure  lush spaces        font style='font-size:12px;'> 2010/12/3
Let X be a Banach space which is lush. It is shown that if a subspace of X is either an L-summand or an M-ideal then it is also lush.
Local Structure of Moduli Spaces      boundedness  connections  differential operators  good quotients       font style='font-size:12px;'> 2010/12/3
We provide a sketch of the GIT construction of the moduli spaces for the three classes of connections: the class of meromorphic connections with fixed divisor of poles D and its subclasses of integrab...
Algebraic Structure on Dirichlet Spaces     Dirichlet form  Markovian property  Algebra       font style='font-size:12px;'> 2007/12/13
In this short note, we shall give a few equivalent conditions for a closed form to be Markovian, and prove that the closure of a sub-algebra of bounded functions in a Dirichlet space must be Markovian...

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