23 citations · 69 across the 15 of their papers we have counts for
15 papers
The continuous functional calculus in Lean
Anatole Dedecker, Jireh Loreaux
The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially -algebras. Here we document our formalization…
k1-injectivity of the Paschke dual algebra for certain simple C*-algebras
Jireh Loreaux, P. W. Ng, Arindam Sutradhar
Let be a nonunital separable simple stable C*-algebra with strict comparison of positive elements and having finite extreme boundary, and let $\mathc…
On commutators of compact operators via block tridiagonalization: generalizations and limitations of Anderson's approach
Jireh Loreaux, Sasmita Patnaik, Srdjan Petrovic +1
We offer a new perspective and some advances on the 1971 Pearcy--Topping problem: Is every compact operator a commutator of compact operators? Our goal is to analyze and generalize…
Closedness of the orbit-closed -numerical range and submajorization
Jireh Loreaux, Sasmita Patnaik
For a positive trace-class operator and a bounded operator , we provide an explicit description of the closure of the orbit-closed -numerical range of in terms of tho…
-injectivity of the Paschke dual algebra, and uniqueness
Jireh Loreaux, P. W. Ng, Arindam Sutradhar
We prove that a large class of Paschke dual algebras of simple unital C*-algebras are -injective. As a consequence, we obtain interesting -uniqueness theorems which genera…
Matrix splitting and ideals in
Jireh Loreaux, Gary Weiss
We investigate the relationship between ideal membership of an operator and its pieces relative to several canonical types of partitions of the entries of its matrix representation…
Convexity of the orbit-closed -numerical range and majorization
Jireh Loreaux, Sasmita Patnaik
We introduce and investigate the orbit-closed -numerical range, a natural modification of the -numerical range of an operator introduced for trace-class by Dirr and vom E…
On diagonals of operators: selfadjoint, normal and other classes
Jireh Loreaux, Gary Weiss
We provide a survey of the current state of the study of diagonals of operators, especially selfadjoint operators. In addition, we provide a few new results made possible by recent…
Remarks on Essential Codimension
Jireh Loreaux, Ping W. Ng
We look for generalizations of the Brown-Douglas-Fillmore essential codimension result, leading to interesting local uniqueness theorems in -theory. We also study the structure…
Traces on ideals and the commutator property
Jireh Loreaux, Gary Weiss
We propose a new class of traces motivated by a trace/trace class property discovered by Laurie, Nordgren, Radjavi and Rosenthal concerning products of operators outside the trace…
Restricted diagonalization of finite spectrum normal operators and a theorem of Arveson
Jireh Loreaux
Kadison characterized the diagonals of projections and observed the presence of an integer. Arveson later recognized this integer as a Fredholm index obstruction applicable to any…
Kadison's Pythagorean Theorem and essential codimension
Victor Kaftal, Jireh Loreaux
Kadison's Pythagorean theorem (2002) provides a characterization of the diagonals of projections with a subtle integrality condition. Arveson (2007), Kaftal, Ng, Zhang (2009), and…
Thompson's theorem for compact operators and diagonals of unitary operators
John Jasper, Jireh Loreaux, Gary Weiss
As applications of Kadison's Pythageorean and carpenter's theorems, the Schur-Horn theorem, and Thompson's theorem, we obtain an extension of Thompsons theorem to compact operators…
Diagonality and idempotents with applications to problems in operator theory and frame theory
Jireh Loreaux, Gary Weiss
We prove that a nonzero idempotent is zero-diagonal if and only if it is not a Hilbert-Schmidt perturbation of a projection, along with other useful equivalences. Zero-diagonal ope…
Majorization and a Schur-Horn Theorem for positive compact operators, the nonzero kernel case
Jireh Loreaux, Gary Weiss
Schur-Horn theorems focus on determining the diagonal sequences obtainable for an operator under all possible basis changes, formally described as the range of the canonical condit…