Partial *-algebras of closed operators and their commutants. I. General structure
Partial *-algebras of closed operators and their commutants. II. Commutants and bicommutants
Quantized fields and operators on a partial inner product space
Quasi *-algebras and generalized inductive limits of C*-algebras
A generalized procedure for the construction of the inductive limit of a family of C*-algebras is proposed. The outcome is no more a C*-algebra but, under certain assumptions, a locally convex quasi *-algebra, named a C*-inductive quasi *-algebra. The properties of positive functionals and representations of C*-inductive quasi *-algebras are investigated, in close connection with the corresponding properties of positive functionals and representations of the C*-algebras that generate the structure....
Quasi *-algebras of measurable operators
Non-commutative -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra...
Quasi *-algebras valued quantized fields
Representation of linear functional by a trace on algebras of unbounded operators defined on dualmetrizable domains
Representations of modules over a *-algebra and related seminorms
Representations of a module over a *-algebra are considered and some related seminorms are constructed and studied, with the aim of finding bounded *-representations of .
*-Representations, seminorms and structure properties of normed quasi *-algebras
The class of *-representations of a normed quasi *-algebra (𝔛,𝓐₀) is investigated, mainly for its relationship with the structure of (𝔛,𝓐₀). The starting point of this analysis is the construction of GNS-like *-representations of a quasi *-algebra (𝔛,𝓐₀) defined by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms defines some seminorms (in some cases, C*-seminorms) that provide useful information on the structure of (𝔛,𝓐₀) and on the continuity...
Spectral trajectories,duality and inductive-projective limits of Hilbert spaces
Spectral well-behaved *-representations
In this brief account we present the way of obtaining unbounded *-representations in terms of the so-called "unbounded" C*-seminorms. Among such *-representations we pick up a special class with "good behaviour" and characterize them through some properties of the Pták function.
Standard generalized vectors for partial O*-algebras
Standard generalized vectors in the space of Hilbert-Schmidt operators
The partial-isometric crossed products of by the forward and backward shifts.
Towards a "Matrix Theory" for Unbounded Operator Matrices.
Unbounded -seminorms, biweights, and -representations of partial -algebras: A review.
Unbounded conditional expectations for partial -algebras.
Unbounded *-representations of tensor product locally convex *-algebras induced by unbounded C*-seminorms
The existence of unbounded *-representations of (locally convex) tensor product *-algebras is investigated, in terms of the existence of unbounded *-representations of the (locally convex) factors of the tensor product and vice versa.
Zero product preservers and orthogonality preservers on algebras of unbounded operators.