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Operator theory, operator algebras and their interactions with geometry and topology. Ronald G. Douglas memorial volume. Proceedings of the international workshop on operator theory and applications (IWOTA 2018), Shanghai, China, July 23–27, 2018. (English) Zbl 1455.47001

Operator Theory: Advances and Applications 278. Cham: Birkhäuser (ISBN 978-3-030-43379-6/hbk; 978-3-030-43382-6/pbk; 978-3-030-43380-2/ebook). x, 534 p. (2020).

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Publisher’s description: This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.
The articles of this volume will be reviewed individually.
Indexed articles:
Douglas, Michael R., Following in the footsteps of Ronald G. Douglas, 1-9 [Zbl 1452.01032]
Ball, Joseph A.; Sau, Haripada, Functional models for commuting Hilbert-space contractions, 11-54 [Zbl 1481.47011]
Benhida, Chafiq; Curto, Raul E., The extended Aluthge transform, 55-76 [Zbl 1507.47048]
Bownik, Marcin; Rzeszotnik, Ziemowit, Open problems in wavelet theory, 77-100 [Zbl 1459.42050]
Brown, Lawrence G., When is every quasi-multiplier a multiplier?, 101-110 [Zbl 1468.46057]
Dai, Xingde; Huang, Wei; Li, Zhongyan, Isomorphism in wavelets. II, 111-127 [Zbl 1458.42025]
Davidson, Kenneth R.; Shamovich, Eli, Nevanlinna-Pick families and singular rational varieties, 129-145 [Zbl 1507.47035]
Das, B. Krishna; Debnath, Ramlal; Sarkar, Jaydeb, On certain commuting isometries, joint invariant subspaces and \(C^\ast \)-algebras, 147-170 [Zbl 1508.47009]
Frymark, Dale; Liaw, Constanze, Spectral analysis, model theory and applications of finite-rank perturbations, 171-202 [Zbl 1507.47028]
Gernandt, H.; Moalla, N.; Philipp, F.; Selmi, W.; Trunk, C., Invariance of the essential spectra of operator pencils, 203-219 [Zbl 1507.47005]
Ghara, Soumitra; Misra, Gadadhar, Decomposition of the tensor product of two Hilbert modules, 221-265 [Zbl 1514.47046]
Gong, Guihua; Jiang, Chunlan; Wang, Kun, A survey on classification of \(C^\ast \)-algebras with the ideal property, 267-287 [Zbl 1468.46066]
Guo, Kunyu; Wang, Yi, A survey on the Arveson-Douglas conjecture, 289-311 [Zbl 1507.47020]
Gurevich, Shamgar; Howe, Roger, The Pieri rule for \(\mathrm{GL}_n\) over finite fields, 313-332 [Zbl 07299684]
ter Horst, S.; Klem, E. M., Cauchy-Riemann equations for free noncommutative functions, 333-357 [Zbl 1468.46070]
Ji, Ronghui; Yu, Guoliang, Uniform Roe algebras and geometric RD property, 359-371 [Zbl 1468.46075]
Jiang, Chunlan; Ji, Kui, Integral curvature and similarity of Cowen-Douglas operators, 373-390 [Zbl 1482.47032]
Jiang, Yongle; Nowak, Piotr W., Singular subgroups in \(\widetilde{A}_2\)-groups and their von Neumann algebras, 391-402 [Zbl 1468.46065]
Mesland, Bram; Şengün, Mehmet Haluk; Wang, Hang, A K-theoretic Selberg trace formula, 403-424 [Zbl 1461.58005]
Misra, Gadadhar; Upmeier, Harald, Singular Hilbert modules on Jordan-Kepler varieties, 425-453 [Zbl 1462.32027]
Park, Efton, A survey of Ron Douglas’s contributions to the index theory of Toeplitz operators, 455-465 [Zbl 1455.47030]
Shin, Chang Eon; Sun, Qiyu, Differential subalgebras and norm-controlled inversion, 467-485 [Zbl 1468.46055]
Tran, Mai; Yang, Rongwei, Hermitian metrics on the resolvent set and extremal arc length, 487-499 [Zbl 1495.47019]
Voiculescu, Dan-Virgil, Hybrid normed ideal perturbations of \(n\)-tuples of operators. II: Weak wave operators, 501-510 [Zbl 1455.47029]
Wang, Kai, An introduction to curvature inequalities for operators in the Cowen-Douglas class, 511-519 [Zbl 1460.47010]
Yang, Liming, Reproducing kernel of the space \(R^t(K, \mu)\), 521-534 [Zbl 1495.47021]

MSC:

47-06 Proceedings, conferences, collections, etc. pertaining to operator theory
00B25 Proceedings of conferences of miscellaneous specific interest
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
46L05 General theory of \(C^*\)-algebras
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
47A13 Several-variable operator theory (spectral, Fredholm, etc.)
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47A15 Invariant subspaces of linear operators
47A45 Canonical models for contractions and nonselfadjoint linear operators
47B13 Cowen-Douglas operators

Biographic References:

Douglas, Ronald George
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