## oa.operator algebras – Trying to understand Haagerup tensor product \$B(H)otimes_{rm h}B(K)\$

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 and compact operators on $$H$$?

Can someone explain me what is $$B(H)otimes_{rm h}B(K)$$ and $$B(H)otimes_{rm h}K(H)$$? Are these spaces completely isometric to some well known operator space?

Is there any reference/lecture notes where I can find these kind of stuff?

P.S: The same question was first asked on MSE here.

## Algebra structure on Haagerup Tensor Product by Operator Spaces

To let $$A$$ and $$B$$ Be operator rooms. Is there an algebra structure on the Haagerup tensor product of operator spaces, so that the Haagerup tensor product becomes Banach algebra?

References or ideas?

## To Haagerup \$ L ^ {P} \$ spaces

There is a definition in Haagerup's article $$L ^ {P}$$ Spaces for weights, my question has become half after setting the standard $$L ^ {P}$$ Place on the crossed product? I'm not clear, please help. How the norm refers to L ^ {P} on weight $$varphi$$?