#### Overview of published works

*The bibliographical references in the text below are found in the
enclosed list of
works. *

**The theory of principal modules and its applications to the study
of regular operators**: [16] - [19], [21], [23], [24], [28], [32], [34],
[35], [52], the book [3].

The notion of a principal module was introduced in the INCREST preprint
62/1980 *Strongly lattice ordered modules over function algebras*
(published at a later date as [17] and [18]). The theory of principal modules
comprises two components : the study of algebraic and topological properties
of these modules; the study of principal modules of linear operators.
In the INCREST preprint 100/1981 *Extension theorems for strongly
lattice - ordered modules and applications to linear operators* the
principality permanence theorem was proved. The theorem was also stated
in [16], [19], [21]. A systematic study of the applications of the permanence
theorem to majorization problems in operator theory has been done. These
problems, which received consideration from the part of many researchers
during the past decade, had as a general theme the discovery of subclasses
*C* of *L*_{r}(E,F) with the property that the relations
0 <= *S* <= *T*, *S* belongs to *L*_{r}(E,F)
and *T* belongs to *C* imply *S* belongs to
*C*. As classical examples of majorization theorems, one could mention
the theorem of Dodds and Fremlin on compact operators and the theorem of
Lozanovskii, Buhvalov and Schep on band properties of the space of integral
operators. Although the statements of these two theorems have in common
the aspect proper to a majorization problem, their original proofs have
very few things in common. By using the permanence theorem of the theory
of principal modules it was possible to elaborate a unified method for
the study of majorization problems which allowed to redemonstrate, on a
common basis, most of the known majorization theorems (in particular the
ones mentioned above) and to find new results.
Among the new results found with the aid of that method, one mentions
the results in [19] and [28] on approximable operators and the results
in [19], [21] and [28] on the relation between the order ideal and the
closed algebraic ideal generated by a regular operator.
**The theory of oru-compact operators**: [29], [33], [36].

A class of regular operators which possess moduli even if the target
space is not order complete.
General theory, the relation with almost integral operators in the
sense of G. Ya. Lozanovskii, the relation with integral operators.
**The theory of strongly latticial classes**: [35].

Methods of construction of spaces of regular operators which possess
moduli and their applications to majorization problems.
**Contributions to the study of integral operators**: [29], [34],
[36], [40], [41], [52].

Contributions to the problems of the intrinsic characterization of
integral operators and of the characterization of some particular classes
of integral operators (Carleman, Hilbert-Schmidt) in terms of algebraic
ideal properties.
The theory of Convolution Type Operators, which provides a unified
framework for the study of order properties of several classes of operators
including integral, convolution, change of variable operators and Radon
transforms.
**Contributions to the theory of factorization of compact operators**:
[39], [44].

**Contributions to the study of abstract Riesz spaces and of the operators
on these spaces**.

The Riesz decomposition property for complex Riesz spaces [7], the
construction of the perfect M-tensor product [16], the relation between
almost integral operators and finite rank operators [34], the extension
of Riesz space valued operators [6], [10], the extension of operators invariant
with respect to a semigroup [5], [10], the relation between the weak Fatou
property and the Egoroff property [22], the integral representation of
regular operators (the book [3]).
**Contributions to the mathematical theory of music**: [11] - [15],
[20], [25], [27], [30], [31], [38], [43], [46] - [49], [54], the textbook
[2].

The applications of algebraic structures (especially groups and their
actions) and of discrete harmonic analysis to music theory, searching for
adequate mathematical modeling of some classes of musical phenomena, especially
those involving periodicity. In this context a model [26] intended for
the study of periodic rhythm was proposed.
The study in four parts *Supplementary Sets and Regular Complementary
Unending Canons*, published in *Perspectives of New Music*, is
concerned with the applications of discrete harmonic analysis (convolution
and Fourier transform on the groups **Z**_{n} ) to the
theory of unending rhythmic canons. The notion of supplementary sets turned
out to be a mathematical model adequate for the study of the regularity
properties and the construction of the named canons.
**Other contributions**.

Measure theory, differential manifolds, topological groups, the theory
of Alfsen and Effros, operatorial characterizations of Hilbert spaces,
reflexive spaces of operators on Hilbert spaces.