Representation of contractively complemented Hilbertian operator spaces and the Fock space

Classification of contractively complemented Hilbertian operator spaces

We construct some separable infinite dimensional homogeneous Hilbertian operator spaces which generalize the row and column spaces R and C. We show that separable infinite-dimensional Hilbertian JC*-triples are completely isometric to an element of the set of (infinite) intersections of these spaces. This set includes the operator spaces R, C, their intersection, and the space spanned by creation operators on the full anti-symmetric Fock space. In fact, we show that these new spaces are completely isometric to the space of creation (resp. annihilation) operators on the anti-symmetric tensors o…

Contractively complemented subspaces of pre-symmetric spaces

In 1965, Ron Douglas proved that if $X$ is a closed subspace of an $L^1$-space and $X$ is isometric to another $L^1$-space, then $X$ is the range of a contractive projection on the containing $L^1$-space. In 1977 Arazy-Friedman showed that if a subspace $X$ of $C_1$ is isometric to another $C_1$-space (possibly finite dimensional), then there is a contractive projection of $C_1$ onto $X$. In 1993 Kirchberg proved that if a subspace $X$ of the predual of a von Neumann algebra $M$ is isometric to the predual of another von Neumann algebra, then there is a contractive projection of the predual of…

Remarks on complemented subspaces of von-Neumann algebras

In this note we include two remarks about bounded ($\underline{not}$ necessarily contractive) linear projections on a von Neumann-algebra. We show that if $M$ is a von Neumann-subalgebra of $B(H)$ which is complemented in B(H) and isomorphic to $M \otimes M$ then $M$ is injective (or equivalently $M$ is contractively complemented). We do not know how to get rid of the second assumption on $M$. In the second part,we show that any complemented reflexive subspace of a $C^*$- algebra is necessarily linearly isomorphic to a Hilbert space.

非交换 $\mathrm{L}^p$-空间上的可压缩分解投影

Contractively decomposable projections on noncommutative $\mathrm{L}^p$-spaces

本文刻画非交换 $\mathrm{L}^p$-空间上的可压缩分解投影，利用新的映射提升定理与遍历理论工具，建立其与 $\mathrm{W}^*$-TRO、$\mathrm{JBW}^*$-三元组及相关 $\mathrm{L}^p$-空间的联系。

半希尔伯特空间中算子和的$A$-范数与$A$-数值半径的不等式及其应用

Inequalities for the $A$-Norm and $A$-Numerical Radius of Operator Sums in Semi-Hilbertian Spaces with Applications

本文对半希尔伯特空间中算子和的$A$-范数与$A$-数值半径建立新不等式，改进广义三角不等式并给出算子乘积与交换子的新边界，可应用于量子力学和偏微分方程，证明了不等式的最优性与优势。

The number of closed ideals in $L(L_p)$

We show that there are $2^{2^{\aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\not= 2<\infty$. This solves a problem in A. Pietsch's 1978 book "Operator Ideals". The proof is quite different from other methods of producing closed ideals in the space of bounded operators on a Banach space; in particular, the ideals are not contained in the strictly singular operators and yet do not contain projections onto subspaces that are non Hilbertian. We give a criterion for a space with an unconditional basis to have $2^{2^{\aleph_0}}$ closed ideals in terms of the existence …