On strictly cyclic algebras, $\mathcal{P}$-algebras and reflexive operators
On strictly cyclic algebras, $\mathcal{P}$-algebras and reflexive operators
An operator algebra $\mathfrak {A} \subset \mathcal {L}(\mathcal {X})$ (the algebra of all operators in a Banach space $\mathcal {X}$ over the complex field C) is called a âstrictly cyclic algebraâ (s.c.a.) if there exists a vector ${x_0} \in \mathcal {X}$ such that $\mathfrak {A}({x_0}) = \{ A{x_0}:A \in \mathfrak …