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In: Mathematica Slovaca, vol. 69, no. 2
Vasile Lauric

# Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class

## Details:

Year, pages: 2019, 433 - 436
Keywords: almost normal operators, quasicentral approximate units

Conjecture 4 of Voiculescu implies that almost normal operators must satisfy a Fuglede-Putnam theorem, namely $[T*,X]$ is a Hilbert-Schmidt operator whenever $[T,X]$ is in the same class for an arbitrary operator $X$. In this note, a partial answer to this question is given, namely when $X\in\mathcal{C}4$, the Fuglede-Putnam theorem holds.

## How to cite:

ISO 690:
Lauric, V. 2019. Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class. In Mathematica Slovaca, vol. 69, no.2, pp. 433-436. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0235

APA:
Lauric, V. (2019). Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class. Mathematica Slovaca, 69(2), 433-436. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0235