Finding a solutions for an equation

fa.purposeful evaluation – occasion of a ‘feeble’ mannequin which isn’t an mannequin? retort

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fa.purposeful evaluation – occasion of a ‘feeble’ mannequin which isn’t an mannequin?

Let $V=B(H,Ok)(H neq Ok)$. A sub house $I$ is named an mannequin of $V$ if $$IV^*V+VV^*I subset I$$ and $I$ is named feeble mannequin of $V$ If $$textual content{span}{IV^*V-VV^*I} subset I$$ It is limpid that each mannequin is feeble mannequin.

Does there animate a feeble mannequin of $B(H,Ok)$ which isn’t an mannequin?

I used to be attempting to assemble occasion from rectangular matrices by having vestige in mind however couldn’t purchase any thought. Any concepts to assemble such mannequin?

P.S. This query was first posted on MSE however I didn’t purchase any retort there.

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