We give definitions and some properties of the shift operator SL(H2) and multiplication operator on L(H ). In addition, we obtain some properties of the commutant of the shift operator SL(H2) and characterize SL(H2)-invariant subspaces.

We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using language commutant algebras, algebra all operators that commute with each term or gate circuit. provide a precise definition this formalism as case where dimension grows exponentially system size. Fragmentation can hence be distinguished from conventional symmetries such $U(1)$ $SU(2...

The description of all solutions to the relaxed commutant lifting problem in terms of an underlying contraction, obtained earlier in joint work of the author with A.E. Frazho and M.A. Kaashoek, is transformed into a linear fractional Redheffer state space form. Under certain additional conditions the coefficient functions in this representation are described explicitly in terms of the original ...