arXiv subjects

Luo Yi Shi

Publications and source records attributed to Luo Yi Shi.

4 recordsLinked to original sources

arXiv2010

Invariant and hyperinvariant subspaces for amenable operators

There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture is equivalent to every non-scalar amenable operator has a non-trivial hyperinvariant subspace and equivalent to every amenable operator is similar to a reducible operator and has a non-trivial invariant subspace; and then, we give two decompositions for amenable operators, which supporting the conjecture.

math.FA↗

arXiv2010

An example of weakly amenable and character amenable operator

A complete characterization of Hilbert space operators that generate weakly amenable algebras remains open, even in the case of compact operator. Farenick, Forrest and Marcoux proposed the question that if $T$ is a compact weakly amenable operator on a Hilbert space $\mathfrak{H}$, then is $T$ similar to a normal operator? In this paper we demonstrate an example of compact triangular operator on infinite-dimension Hilbert space which is a weakly amenable and character amenable operator but is not similar to a normal operator.

math.FA↗

arXiv2010

Cocycle perturbation on Banach algebra

Let $α$ be a flow on a Banach algebra $\mathfrak{B}$, and $t\longmapsto u_t$ a continuous function on $\mathbb{R}$ into the group of invertible elements of $\mathfrak{B}$ such that $u_sα_s(u_t )=u_{s+t}, s, t \in \mathbb{R}$. Then $β_t=$Ad$u_t\circα_t, t\in \mathbb{R}$ is also a flow on $\mathfrak{B}$. $β$ is said to be a cocycle perturbation of $α$. We show that if $α,β$ are two flows on nest algebra (or quasi-triangular algebra), then $β$ is a cocycle perturbation of $α$. And the flows on nest algebra (or quasi-triangular algebra) are all uniformly continuous.

math.OA↗

arXiv2010

Generalized notions of character amenability

In this paper the concepts of character contractibility, approximate character amenability (contractibility) and uniform approximate character amenability (contractibility) are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebra. We prove that approximate character amenability and approximate character contractibility are the same properties, as are uniform approximate character amenability and character amenability, as are uniform approximate character contractibility and character contractibility. For commutative Banach algebra, we prove that character contractibility and contractibility are the same properties. Moreover, general theory for those concepts is developed.

math.FA↗