# zbMATH — the first resource for mathematics

Unitary equivalence of sets of self-adjoint operators. (English. Russian original) Zbl 0648.47023
Funct. Anal. Appl. 14, No. 1, 48-50 (1980); translation from Funkts. Anal. Prilozh. 14, No. 1, 60-62 (1980).
Let H be a Hilbert space. The authors show that the problem of the unitary equivalence of two bounded sequences $$\{A_ k\}$$, $$\{B_ k\}$$ of selfadjoint operators is equivalent to the same problem for two pairs $$\{A_ 1,A_ 2\}$$, $$\{B_ 1,B_ 2\}$$ of bounded selfadjoint operators, or for two triples of orthogonal projections.

##### MSC:
 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) 47A65 Structure theory of linear operators
Full Text:
##### References:
 [1] P. R. Halmos and J. E. McLaughlin, Pac. J. Math.,13, 585–596 (1963). · Zbl 0189.13402 · doi:10.2140/pjm.1963.13.585 [2] I. M. Gel’fand and V. A. Ponomarev, Funkts. Anal. Prilozhen.,3, No. 4, 81–82 (1969). · doi:10.1007/BF01674013 [3] J. Ernest, Mem. Am. Math. Soc.,6, No. 171 (1976). [4] V. Ya. Golodets, Usp. Mat. Nauk,24, No. 4, 3–64 (1969). [5] R. V. Douglas and C. Pearcy, Mich. Math. J.,16, 21–24 (1969). · Zbl 0175.44301 · doi:10.1307/mmj/1029000161 [6] E. A. Morozova and N. N. Chentsov, ”Unitary equivariant families of subspaces,” Preprint, Inst. Prikl. Mat., No. 52, Moscow (1974).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.