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Recall that a ternary ring of operators (TRO) is a closed subspace $Z$ of $C^*$-algebra such that $xy^*z \in V$ for all $x,y,z \in Z$. How does one defines positivity/ordering in TRO? I tried to …

For Hilbert spaces $H$ and $K$, let $V=B(H,K)(H \neq K)$. A sub space $I$ of $V$ is called an ideal of $V$ if $$IV^*V+VV^*I \subset I$$ and $I$ is called weak ideal of $V$ If $$\text{span}\{IV^*V-VV^* …

Let $V$ be a Ternary rings of operators(TRO) i.e. closed subspace of $B(H,K)$ such that $xy^*z \in V$ for all $x,y,z \in V$. A subspace $I$ of $V$ is called a left (right)TRO ideal provided $VV^*I \su …

The following question was first posted on Math.Stackexchange.com but unfortunately I didn’t get any answer. This might be obvious for many researchers but I can’t see how this is so, thus I am asking …

From one of the talks I attended long back, I vaguely seem to remember the following fact: Let $A$ and $B$ be $C^{\ast}$-algebras. If either $A$ is exact or $B$ is nuclear then every closed ideal of …

Let $A$ and $B$ be $C^{\ast}$-algebras with centers $Z$ and $Z'$ respectively. Let $\phi:A \to B$ be surjective $C^{\ast}$-morphism. Then $\phi(Z)=Z'$ if and only if the map $\Phi: \operatorname{Prim …

I'm interested in learning about ternary Banach Algebras ( mainly ideal theory and tensor product) Can someone please recommend me some papers/ books/ notes which deals with mentioned topics? Thank …

Let $H$ and $K$ be Hilbert spaces. Recall that a closed subspace $V\subset B(H,K)$ is called a ternary ring of operators(TRO) if $xy^*z \in V$ for all $x,y,z \in V$. Obviously a TRO is also a operato …

I’m self reading Haagerup tensor product of operator spaces. Understanding it properly, I’m trying some examples. Let $H$ And $K$ be Hilbert space. Let $B(H)$ and $K(H)$ denotes the spaces of bounded …

Let $(A_n, \phi_n)$ be an inductive system of $C^*$ algebras. It's well known double dual of $C^*$-algebra is again a $C^*$ algebra. Is it true that $\varinjlim A_n^{**}=(\varinjlim A_n)^{**}$ Can s …

Recall that a ternary $C^*$-ring is a complex Banach space $X$, equipped with a associative ternary product $[.,.,.]:X^3 \to X$ which is linear in outer variables and conjugate linear in middle varia …

Let $A$ and $B$ denote $C^{\ast}$-algebras. Let $\lVert\cdot\rVert_h$ and $\lVert\cdot\rVert_{\text {max}}$ denote the Haagerup norm and max $C^*$-norms on $ A \otimes B$, respectively. I am looking f …

Let $V $ be a ternary ring of operator(TRO) and $B $ be a $\mathbb {C}^{\ast} $-algebra. Let $V \otimes^hB $ denotes the Haagerup tensor product of $V $ and $B $. Obviously if $V $ or $B $ is $\mathbb …

A ternary $C^{\ast}$-ring is a complex Banach space $X$, equipped with a ternary product $[\cdot,\cdot,\cdot]:X^3 \to X$ which is linear in outer variables and conjugate linear in middle variable. Al …

Let $H$ and $K$ be Hilbert spaces. Recall that a Ternary ring of operator(TRO) $V$ is a closed subspace of $B(H,K)$ such that $xy^{\ast}z \in V$ for all $x,y,z \in V$. I have recently started reading …