Let $H$ be separable Hilbert space. Let $A$ be a maximal abeliean Von abelian von Neumann algebra subalgebra of $B(H)$, and $B$ an abeliean Von abelian von Neumann algebra with $A\cap B={\mathbb C}I$, where $I$ is the indentity element of $B(H)$. Are Does there exist another maximal abeliean Von abelian von Neumann algebra, subalgebra of $B(H)$, say $C$, such that $C\supseteq B$ and $A\cap C={\mathbb C}I$?
Let $H$ be separable Hilbert space. Let $A$ be a maximal abeliean Von Neumann algebra of $B(H)$, and $B$ an abeliean Von Neumann algebra with $A\cap B={\mathbb C}I$, where $I$ is the indentity element of $B(H)$. Are there exist another maximal abeliean Von Neumann algebra, say $C$, such that $C\supseteq B$ and $A\cap C={\mathbb C}I$?