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Carvalho, L., Diogo, C., Mendes, S. & Soares, H. (2024). A note on the essential numerical range of block diagonal operators. Forum Mathematicum. 36 (5), 1147-1157
L. C. Carvalho et al., "A note on the essential numerical range of block diagonal operators", in Forum Mathematicum, vol. 36, no. 5, pp. 1147-1157, 2024
@article{carvalho2024_1781499563829,
author = "Carvalho, L. and Diogo, C. and Mendes, S. and Soares, H.",
title = "A note on the essential numerical range of block diagonal operators",
journal = "Forum Mathematicum",
year = "2024",
volume = "36",
number = "5",
doi = "10.1515/forum-2023-0166",
pages = "1147-1157",
url = "https://www.degruyter.com/journal/key/form/html"
}
TY - JOUR
TI - A note on the essential numerical range of block diagonal operators
T2 - Forum Mathematicum
VL - 36
IS - 5
AU - Carvalho, L.
AU - Diogo, C.
AU - Mendes, S.
AU - Soares, H.
PY - 2024
SP - 1147-1157
SN - 0933-7741
DO - 10.1515/forum-2023-0166
UR - https://www.degruyter.com/journal/key/form/html
AB - In this note, we characterize the essential numerical range of a block diagonal operator T = ?i Ti in terms of the numerical ranges {W(Ti)}i of its components. Specifically, the essential numerical range of T is the convex hull of the limit superior of {W(Ti)}i. This characterization can be simplified further. In fact, we prove the existence of a decomposition of T for which the convex hull is not required.
ER -
English