BUG: for DataFrame subclass, astype with dict does not keep the subclass

[mitar]

• I have checked that this issue has not already been reported.
• I have confirmed this bug exists on the latest version of pandas.

Code Sample, a copy-pastable example

import numpy
import pandas

class CustomDataFrame(pandas.DataFrame):
    @property
    def _constructor(self) -> type:
        return CustomDataFrame

a = CustomDataFrame({'a': [1,2,3], 'b': ['A','B','C']})

print(type(a))

b = a.astype({'a': numpy.int64, 'b': object})

print(type(b))

Problem description

If I use astype on a DataFrame subclass, I would expect that the DataFrame class do not change, and only dtypes of columns change.

Expected Output

<class '__main__.CustomDataFrame'>
<class '__main__.CustomDataFrame'>

But I get:

<class '__main__.CustomDataFrame'>
<class 'pandas.core.frame.DataFrame'>

Output of pd.show_versions()

INSTALLED VERSIONS

commit : f2c8480
python : 3.8.5.final.0
python-bits : 64
OS : Linux
OS-release : 5.8.0-48-generic
Version : #54~20.04.1-Ubuntu SMP Sat Mar 20 13:40:25 UTC 2021
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.2.3
numpy : 1.20.2
pytz : 2021.1
dateutil : 2.8.1
pip : 20.0.2
setuptools : 44.0.0
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fsspec : None
fastparquet : None
gcsfs : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
numba : None

[EmilianoJordan]

This exact issue is caused in the above example by not defining a sub classed Series and the _constructor_sliced property on the CustomDataFrame. For example this code works as expected:

import numpy
import pandas as pd


class SubclassedSeries(pd.Series):
    @property
    def _constructor(self):
        return SubclassedSeries

    @property
    def _constructor_expanddim(self):
        return SubclassedDataFrame


class SubclassedDataFrame(pd.DataFrame):
    @property
    def _constructor(self):
        return SubclassedDataFrame

    @property
    def _constructor_sliced(self):
        return SubclassedSeries


a = SubclassedDataFrame({'a': [1,2,3], 'b': ['A','B','C']})

b = a.astype({'a': numpy.int64, 'b': object})

assert isinstance(b, SubclassedDataFrame)

This exact issue could be solved in NDFrame.astype but I imagine that a sub classed DataFrame and sub classed Series are intertwined in a lot more places than just astype. My suggestion, and I'd be happy to implement it, would be to note this behavior in the docs and that both sub classed types need to be implemented.