Additive maps onto matrix spaces compressing the spectrum
نویسندگان
چکیده
منابع مشابه
A Note on Spectrum Preserving Additive Maps on C*-Algebras
Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.
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Let A be a set of N matrices. Let g(A): = |A + A| + |A · A|, where A+A = {a1 +a2 | ai ∈ A} and A ·A = {a1a2 | ai ∈ A} are the sumset and productset. We prove that if the determinant of the difference of any two distinct matrices in A is nonzero, then g(A) cannot be bounded below by cN for any constant c. We also prove that if A is a set of d× d symmetric matrices, then there exists ε = ε(d) > 0...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2016
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2016.01.048