The Classical Smith-Ward Problem
Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.
Statement
The Smith-Ward theorem realizes the first essential matrix ranges of an operator as the matrix ranges of a compact perturbation. The classical Smith-Ward problem asks whether that perturbation can be chosen independently of , equivalently whether the identity map on a three-dimensional operator system in the Calkin algebra always lifts. It need not: an explicit three-dimensional hyperrigid operator system has no unital completely positive lift, and its dual is the first three-dimensional operator system that fails to be exact.
Context
Harris had settled the generalized problem in dimension four; this reaches dimension three
A named lifting problem in operator algebras with a documented line of attack through Paulsen and more recently Harris.
People
Projects
Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.
Interest
Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.
Attempts
No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
The one-line disclosure says the model was used to perform literature search and to accelerate the search for the operator system. Since that operator system is the counterexample, the contribution touches the mathematics, but the wording does not say the model found it.
Harris had settled the generalized problem in dimension four; this reaches dimension three
Reviews
0 human reviews · 0 machine checksNo person has reviewed this attempt. It has not been checked at all.
Endorsements
0 endorsementsNo one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.
Discussion of this attempt
no comments
Discussion
Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.