What the study found
The study shows that the Schur multiplier norm of a complex self-adjoint matrix can be determined by a minimization formula involving a diagonal matrix. It also gives a corresponding formula for the dual norm of the Schur multiplier norm.
Why the authors say this matters
The authors present these formulas as a way to study the dual norm as a formal linear program. In the abstract, they frame this as a mathematical characterization of the norm and its dual.
What the researchers tested
The paper studies complex self-adjoint n × n matrices and norms on matrices in M(m, n)(C). It defines the dual norm using a trace-based supremum and introduces diagonal matrices built from vectors in C^n and R^n.
What worked and what didn't
For a self-adjoint matrix A, the Schur multiplier norm is given by min{||diag(P)||∞ : -P ≤ A ≤ P}. For the dual norm, the abstract states the formula ||A||S* = min{Tr_n(Δ(λ)) : λ ∈ R^n, -Δ(λ) ≤ A ≤ Δ(λ)}.
What to keep in mind
The abstract only provides the formulas and says the minimization problem is studied as a formal linear program. It does not describe examples, numerical experiments, or broader applications in the available summary.
Key points
- The Schur multiplier norm of a complex self-adjoint matrix has a minimization characterization.
- The dual norm of the Schur multiplier norm is also given by a minimization formula.
- Both formulas use diagonal matrices and inequalities bounding the matrix A.
- The paper studies the minimization problem as a formal linear program.
- The abstract does not describe examples or applications.
Disclosure
- Research title:
- Schur multiplier norm and its dual norm are characterized
- Authors:
- Erik Christensen
- Institutions:
- University of Copenhagen
- Publication date:
- 2026-04-23
- OpenAlex record:
- View
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