ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.24, no.2, pp.253-260, 2016 (SCI-Expanded)
By applying the so-called Berezin symbols method we prove a Gohberg-Krein type theorem on the weak limit of compact operators on the nonstandard reproducing kernel Hilbert space which essentially improves the similar results of Karaev [5]. We also in terms of reproducing kernels and Berezin symbols investigate the structure of invariant subspaces of compact operators.