TY - JOUR
T1 - ON THE STAMPFLI POINT OF SOME OPERATORS AND MATRICES
AU - Quartz, Thanin
AU - Spitkovsky, Ilya M.
N1 - Funding Information:
The results are partially based on the Capstone project of the first named author [TQ] under the supervision of the second named author [IMS]. The latter was also supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.
Publisher Copyright:
© 2021, Element D.O.O.. All rights reserved.
PY - 2021/12
Y1 - 2021/12
N2 - The center of mass of an operator A (denoted St(A), and called in this paper as the Stampfli point of A) was introduced by Stampfli in his Pacific J. Math (1970) paper as the unique λ ∈ C delivering the minimum value of ‖A − λI‖. We derive some results concerning the location of St(A) for several classes of operators, including 2-by-2 block operator matrices with scalar diagonal blocks and 3-by-3 matrices with repeated eigenvalues. We also show that for almost normal A its Stampfli point lies in the convex hull of the spectrum, which is not the case in general. Some relations between the property St(A)=0 and Roberts orthogonality of A to the identity operator are established.
AB - The center of mass of an operator A (denoted St(A), and called in this paper as the Stampfli point of A) was introduced by Stampfli in his Pacific J. Math (1970) paper as the unique λ ∈ C delivering the minimum value of ‖A − λI‖. We derive some results concerning the location of St(A) for several classes of operators, including 2-by-2 block operator matrices with scalar diagonal blocks and 3-by-3 matrices with repeated eigenvalues. We also show that for almost normal A its Stampfli point lies in the convex hull of the spectrum, which is not the case in general. Some relations between the property St(A)=0 and Roberts orthogonality of A to the identity operator are established.
KW - Almost normal operators
KW - Maximal numerical range
KW - Roberts orthogonality
KW - Stampfli point (center of mass) of operators
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U2 - 10.7153/oam-2021-15-80
DO - 10.7153/oam-2021-15-80
M3 - Article
AN - SCOPUS:85126461028
VL - 15
SP - 1267
EP - 1287
JO - Operators and Matrices
JF - Operators and Matrices
SN - 1846-3886
IS - 4
M1 - 15-80
ER -