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Topic · Mathematical Physics

Advanced Banach Space Theory

Advanced Banach Space Theory is a research topic within Mathematical Physics. Science Explorer counts 18k research works in it since 1950. 9.3% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics in the theory of Banach spaces and operators, including functional analysis, topological vector spaces, holomorphic functions, summing operators, Bohr inequality, Lipschitz functions, geometric aspects, and approximation theory.

  • Banach Spaces
  • Operators
  • Functional Analysis
  • Topological Vector Spaces
  • Holomorphic Functions
  • Summing Operators
  • Bohr Inequality
  • Lipschitz Functions
  • Geometric Aspects
  • Approximation Theory
Research works
18k
fractional, since 1950
In the world top 10%
1.6k
per year above
Top-10% rate
9.3%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
-4%
the tick is no change

Which countries lead Advanced Banach Space Theory research?

By volume, China and India publish the most (187 and 161 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 187 works
  2. 2 India 161 works
  3. 3 United States 160 works
  4. 4 Russia 133 works
  5. 5 Spain 128 works
  6. 6 Poland 86 works
  7. 7 Türkiye 75 works
  8. 8 Iran 67 works
  9. 9 France 57 works
  10. 10 Germany 52 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 16.9%India: 14.6%United States: 14.5%Russia: 12.1%6 others listed: 42.0%17%largest
China187 · 16.9%India161 · 14.6%United States160 · 14.5%Russia133 · 12.1%6 others listed463 · 42.0%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Banach Space Theory research?

By volume in 2022–2025, Lomonosov Moscow State University publishes the most Advanced Banach Space Theory research, followed by Universitat Politècnica de València and Institute of Mathematics.

By volume, 2022–2025

  1. 1 Lomonosov Moscow State UniversityRussia 23 works
  2. 2 Universitat Politècnica de ValènciaSpain 21 works
  3. 3 Institute of MathematicsPoland 14 works
  4. 4 Universidad de GranadaSpain 13 works
  5. 5 Moscow Center For Continuous Mathematical EducationRussia 12 works
  6. 6 Charles UniversityCzechia 12 works
  7. 7 Vasyl Stefanyk Carpathian National UniversityUkraine 11 works
  8. 8 University of AlbertaCanada 10 works
  9. 9 Universidad de ExtremaduraSpain 10 works
  10. 10 University of SfaxTunisia 10 works

Who are the leading researchers in Advanced Banach Space Theory?

The most-cited researchers publishing on Advanced Banach Space Theory include Terence Tao.

  1. 1 Terence Tao United States 3.1k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Advanced Banach Space Theory research done?

The largest centres of Advanced Banach Space Theory research in 2022–2025 are Moscow (Russia), Prague (Czechia), Valencia (Spain) and Warsaw (Poland). Among places with at least 20 works in it, it is an unusually large share of all research in Valencia.

Largest cities, 2022–2025

  1. 1 Moscow Russia 57 works
  2. 2 Prague Czechia 31 works
  3. 3 Valencia Spain 28 works
  4. 4 Warsaw Poland 26 works
  5. 5 Beijing China 22 works
  6. 6 Madrid Spain 21 works
  7. 7 Kolkata India 19 works
  8. 8 Vienna Austria 18 works
  9. 9 Tehran Iran 17 works
  10. 10 Paris France 16 works

Where it is the local speciality

  1. ValenciaES · 27.6 works12×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Advanced Banach Space Theory than the world average.

See Advanced Banach Space Theory on the map

Where is the best place to study Advanced Banach Space Theory?

Among universities, judged by research, Lomonosov Moscow State University, Vasyl Stefanyk Carpathian National University and Moscow Center For Continuous Mathematical Education score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 15.6%fractional works in this node (log) →share in the world top 10% →Lomonosov Moscow State University: 23, 19.5%Vasyl Stefanyk Carpathian National University: 11, 45.9%Moscow Center For Continuous Mathematical Education: 12, 25.2%Universitat Politècnica de València: 21, 11.2%University of Sfax: 10, 11.6%Universidad de Granada: 13, 11.2%Charles University: 12, 10.7%Universidad de Extremadura: 10, 8.4%Jadavpur University: 8, 7.9%Adam Mickiewicz University in Poznań: 10, 4.4%Vasyl Stefanyk Carpa…Moscow Center For Co…Lomonosov Moscow Sta…Universitat Politècn…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Lomonosov Moscow State UniversityRussia 68.719.5%14.4×23 +68.0%
2 Vasyl Stefanyk Carpathian National UniversityUkraine 63.745.9%67.8×11 -9.9%
3 Moscow Center For Continuous Mathematical EducationRussia 58.625.2%377.8×12 —
4 Universitat Politècnica de ValènciaSpain 57.011.2%31.7×21 +19.2%
5 University of SfaxTunisia 55.811.6%21.7×10 +217.5%
6 Universidad de GranadaSpain 48.011.2%13.4×13 +21.8%
7 Charles UniversityCzechia 44.210.7%14.4×12 -19.6%
8 Universidad de ExtremaduraSpain 37.68.4%27.9×10 -22.3%
9 Jadavpur UniversityIndia 36.57.9%17.1×8 +50.0%
10 Adam Mickiewicz University in PoznańPoland 35.14.4%13.3×10 +9.2%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Advanced Banach Space Theory research growing?

Output in 2018–2022 was 4% lower than in 2013–2017, peaking in 2025. The fastest-growing topics are Advanced Banach Space Theory.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.