Hilbert space fragmentation is a novel type of ergodicity breaking in closed quantum systems. Recently, an algebraic approach was utilized to provide definition characterizing families Hamiltonian systems based on their (generalized) symmetries. In this paper we reveal simple connection between the aforementioned classification physical and coherence generation properties, quantified by generat...

We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space attached to the dual of the Hilbert space of the representation. This permit...

A 2-Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we deene a 2-Hilbert space to be an abelian category enriched over Hilb with a-structure, conjugate-linear on the hom-sets, satisfying hf g; hi = hg; f hi = hf; hg i. We also deene monoidal, braided monoidal, and symmetric monoidal versions of 2-Hilbert spaces, which we call 2-H...

A 2-Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we define a 2-Hilbert space to be an abelian category enriched over Hilb with a ∗-structure, conjugate-linear on the hom-sets, satisfying 〈fg, h〉 = 〈g, f∗h〉 = 〈f, hg∗〉. We also define monoidal, braided monoidal, and symmetric monoidal versions of 2-Hilbert spaces, which we call ...

We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite tree structure associated with the underlying Hilbert space. These shifts arise naturally through weighted versions of certain representations of the Cuntz C...

In this paper, the notion of operator means in setting JB-algebras is introduced and their properties are studied. Many identities inequalities established, most them have origins from operators on Hilbert space but they different forms connotations, proofs require techniques JB-algebras.