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J. E. Pascoe
J. E. Pascoe
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Let $H$ be a separable Hilbert space. Let $A \subseteq B(H)$ be a finitely generated unital algebra. Let $M$ be the strong operator topology closure of $A.$ Let $B_A$ be the closed ball in $A$ and $B_M$ be the closed ball in $M.$ Is $B_M$ the strong operator topology closure of $B_A?$ (More likely, is there a counterexample?)

Let $H$ be a separable Hilbert space. Let $A \subseteq B(H)$ be a unital algebra. Let $M$ be the strong operator topology closure of $A.$ Let $B_A$ be the closed ball in $A$ and $B_M$ be the closed ball in $M.$ Is $B_M$ the strong operator topology closure of $B_A?$ (More likely, is there a counterexample?)

Let $H$ be a separable Hilbert space. Let $A \subseteq B(H)$ be a finitely generated unital algebra. Let $M$ be the strong operator topology closure of $A.$ Let $B_A$ be the closed ball in $A$ and $B_M$ be the closed ball in $M.$ Is $B_M$ the strong operator topology closure of $B_A?$ (More likely, is there a counterexample?)

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J. E. Pascoe
J. E. Pascoe
  • 1.4k
  • 11
  • 20

The ball formulation of the Kaplansky density theorem in nonselfadjoint algebras

Let $H$ be a separable Hilbert space. Let $A \subseteq B(H)$ be a unital algebra. Let $M$ be the strong operator topology closure of $A.$ Let $B_A$ be the closed ball in $A$ and $B_M$ be the closed ball in $M.$ Is $B_M$ the strong operator topology closure of $B_A?$ (More likely, is there a counterexample?)