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# General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series

### Abstract

We prove that the classical Menshov-Rademacher, Orlicz, and Tandori theorems remain true for orthogonal series given in the direct integrals of measurable collections of Hilbert spaces. In particular, these theorems are true for the spaces $L_{2}(X,d\mu;H)$ of vector-valued functions, where $(X,\mu)$ is an arbitrary measure space, and $H$ is a real or complex Hilbert space of an arbitrary dimension.

### Article Information

 Title General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 330-340 MathSciNet MR2907361 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Aleksandr A. Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Vladimir A. Mikhailets and Aleksandr A. Murach, General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series, Methods Funct. Anal. Topology 17 (2011), no. 4, 330-340.

### BibTex

@article {MFAT608,
AUTHOR = {Mikhailets, Vladimir A. and Murach, Aleksandr A.},
TITLE = {General forms of  the Menshov-Rademacher, Orlicz, and Tandori theorems  on orthogonal series},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {4},
PAGES = {330-340},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=608},
}