Michael A. Dritschel
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Michael A. Dritschel has a total of 31 co-authors. Here are the top co-authors by number of shared publications:
- Dmitry Yakubovich
Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain
6 shared publications - James Rovnyak
University of Virginia
5 shared publications - Daniel Estévez
Oceano Atlantico 38, Tres Cantos, Madrid, Spain
4 shared publications - Scott McCullough
Univ Florida, Dept Math, Gainesville, FL 32611 USA
4 shared publications James Rovnyak
University of Virginia
3 shared publicationsAad Dijksma
University of Groningen, Groningen, Netherlands
2 shared publications
Latest Publications
- Open Access
- 25 February 2026
- Published by Springer Nature in Complex Analysis and Operator Theory
- Vol. 20 (3) , 64
Rearrangement Invariant Orthogonal Sums in Kreĭn Spaces. II
Part I of the paper considered infinite orthogonal sums of regular subspaces in a Kreĭn space (that is, of subspaces which are themselves Kreĭn spaces). How precisely these sums should be defined and conditions for when such sums are themselves regular were determined. These included, for example, a boundedness condition for the sum of the corresponding orthogonal projections. The same problem is addressed here for (quasi-)pseudo-regular subspaces. Such subspaces are orthogonal direct sums of a regular space and isotropic, or neutral, subspaces. Alternate characterizations of such subspaces are given, and infinite orthogonal sums are examined via unconditional, or Moore-Smith, sums of operator ranges.
- 25 February 2026
- Published by Springer Nature in Complex Analysis and Operator Theory
- Vol. 20 (3) , 64
Open AccessRearrangement Invariant Orthogonal Sums in Kreĭn Spaces. II
Part I of the paper considered infinite orthogonal sums of regular subspaces in a Kreĭn space (that is, of subspaces which are themselves Kreĭn spaces). How precisely these sums should be defined and conditions for when such sums are themselves regular were determined. These included, for example, a boundedness condition for the sum of the corresponding orthogonal projections. The same problem is addressed here for (quasi-)pseudo-regular subspaces. Such subspaces are orthogonal direct sums of a regular space and isotropic, or neutral, subspaces. Alternate characterizations of such subspaces are given, and infinite orthogonal sums are examined via unconditional, or Moore-Smith, sums of operator ranges.
- Open Access
Hermitian indices and factorization of selfadjoint operators on a Kreĭn space
The hermitian indices of a selfadjoint operator $C$ on a Kreĭn space $\mathcal H$ are defined as geometric measures of positivity and negativity of the operator. A different pair of indices arises in the Bognár-Krámli factorization of $C$, which writes $C$ as a product $AA^*$ where $A$ acts on a Kreĭn space $\mathcal A$ into $\mathcal H$ and has zero kernel; the new indices are the positive and negative indices of $\mathcal A$. Such factorizations are far from unique. When $\mathcal H$ is separable, it is known that the two notions of indices always coincide, and this has applications to index formulas in the theory of Julia operators and completion problems for operator matrices. A new proof of the equality of indices that does not require separability is given in this work.Open AccessHermitian indices and factorization of selfadjoint operators on a Kreĭn space
The hermitian indices of a selfadjoint operator $C$ on a Kreĭn space $\mathcal H$ are defined as geometric measures of positivity and negativity of the operator. A different pair of indices arises in the Bognár-Krámli factorization of $C$, which writes $C$ as a product $AA^*$ where $A$ acts on a Kreĭn space $\mathcal A$ into $\mathcal H$ and has zero kernel; the new indices are the positive and negative indices of $\mathcal A$. Such factorizations are far from unique. When $\mathcal H$ is separable, it is known that the two notions of indices always coincide, and this has applications to index formulas in the theory of Julia operators and completion problems for operator matrices. A new proof of the equality of indices that does not require separability is given in this work. - Open Access
- 5 September 2024
- Published by Springer Nature in Mathematische Annalen
- Vol. 391 (2) , 3225
Correction: Factoring non-negative operator valued trigonometric polynomials in two variables
- 5 September 2024
- Published by Springer Nature in Mathematische Annalen
- Vol. 391 (2) , 3225
Open AccessCorrection: Factoring non-negative operator valued trigonometric polynomials in two variables
- 8 August 2024
- Published by Springer Nature
- p. 1-21
Contractions and the Commutant Lifting Theorem in Kreı̆n Spaces
- 8 August 2024
- Published by Springer Nature
- p. 1-21
Contractions and the Commutant Lifting Theorem in Kreı̆n Spaces
- Open Access
- 27 June 2024
- Published by Springer Nature in Mathematische Annalen
- Vol. 391 (1) , 515-537
Factoring non-negative operator valued trigonometric polynomials in two variables
It is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree $$(d_1,d_2)$$ can be written as a sum of hermitian squares of at most $$2d_2$$ analytic polynomials.- 27 June 2024
- Published by Springer Nature in Mathematische Annalen
- Vol. 391 (1) , 515-537
Open AccessFactoring non-negative operator valued trigonometric polynomials in two variables
It is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree $$(d_1,d_2)$$ can be written as a sum of hermitian squares of at most $$2d_2$$ analytic polynomials. - Open Access
Factoring Non-negative Operator Valued Trigonometric Polynomials in Two Variables
It is shown using Schur complement techniques that a non-negative operator valued trigonometric polynomial in two variables with degree (d_1,d_2) can be written as a finite sum of hermitian squares of at most 2d_2 analytic polynomials with degrees at most (d_1, 2d_2-1).
Open AccessFactoring Non-negative Operator Valued Trigonometric Polynomials in Two Variables
It is shown using Schur complement techniques that a non-negative operator valued trigonometric polynomial in two variables with degree (d_1,d_2) can be written as a finite sum of hermitian squares of at most 2d_2 analytic polynomials with degrees at most (d_1, 2d_2-1).
- Open Access
- 22 February 2021
- Published by Springer Nature in Complex Analysis and Operator Theory
- Vol. 15 (2) , 1-36
Products of Positive Operators
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class $${\mathcal {L}^{+\,2}}$$ of bounded operators on separable infinite dimensional Hilbert spaces which can be written as the product of two bounded positive operators is studied. The structure is much richer, and connects (but is not equivalent to) quasi-similarity and quasi-affinity to a positive operator. The spectral properties of operators in $${\mathcal {L}^{+\,2}}$$ are developed, and membership in $${\mathcal {L}^{+\,2}}$$ among special classes, including algebraic and compact operators, is examined.- 22 February 2021
- Published by Springer Nature in Complex Analysis and Operator Theory
- Vol. 15 (2) , 1-36
Open AccessProducts of Positive Operators
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class $${\mathcal {L}^{+\,2}}$$ of bounded operators on separable infinite dimensional Hilbert spaces which can be written as the product of two bounded positive operators is studied. The structure is much richer, and connects (but is not equivalent to) quasi-similarity and quasi-affinity to a positive operator. The spectral properties of operators in $${\mathcal {L}^{+\,2}}$$ are developed, and membership in $${\mathcal {L}^{+\,2}}$$ among special classes, including algebraic and compact operators, is examined. - 1 November 2018
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 467 (1) , 95-131
Rational dilation problems associated with constrained algebras
- 1 November 2018
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 467 (1) , 95-131
Rational dilation problems associated with constrained algebras
- 1 July 2018
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 463 (1) , 345-364
Resolvent criteria for similarity to a normal operator with spectrum on a curve
- 1 July 2018
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 463 (1) , 345-364
Resolvent criteria for similarity to a normal operator with spectrum on a curve
- Open Access
Rational dilation problems associated with constrained algebras
It is shown that rational dilation fails on broad collection of distinguished varieties associated to constrained subalgebras of the disk algebra of the form C + B A(D), where B is a finite Blaschke product with two or more zeros. This is accomplished in part by finding a minimal set of test functions. In addition, an Agler-Pick interpolation theorem is given and it is proved that there exist Kaijser-Varopoulos style examples of non-contractive unital representations where the generators are contractions.
Open AccessRational dilation problems associated with constrained algebras
It is shown that rational dilation fails on broad collection of distinguished varieties associated to constrained subalgebras of the disk algebra of the form C + B A(D), where B is a finite Blaschke product with two or more zeros. This is accomplished in part by finding a minimal set of test functions. In addition, an Agler-Pick interpolation theorem is given and it is proved that there exist Kaijser-Varopoulos style examples of non-contractive unital representations where the generators are contractions.