Blog

I have to prove this equation for a task. But, I was stuck here: Open image to know where I was stuckRead more

Let $ \mathcal{B}(F)$ the algebra of all bounded linear operators on a complex Hilbert space $ F$ . Let $ M\in \mathcal{B}(F)^+$ . According to the answer to this question we have: $ $ \mathcal{B}^M(F)\subseteq \mathcal{B}^{M^{1/2}}(F),$ $ where $ $ \mathcal{B}^M(F)=\left\{S\in \mathcal{B}(F):\,\,\,\text{Im}(S^{*}M)\subseteq \text{Im}(M)\right\},$ $ $ $ \mathcal{B}^{M^{1/2}}(F)=\left\{S\in \mathcal{B}(F):\,\,\,\text{Im}(S^{*}M^{1/2})\subseteq \text{Im}(M^{1/2})\right\}.$ $ I hope to get anRead more