BUG: Parameter col_space of to_html method not working with multi-level columns

pandas/io/formats/html.py

@@ -68,10 +68,15 @@ def __init__(
         self.table_id = table_id
         self.render_links = render_links
 
-        self.col_space = {
-            column: f"{value}px" if isinstance(value, int) else value
-            for column, value in self.fmt.col_space.items()
-        }
+        self.col_space = {}
+        for column, value in self.fmt.col_space.items():
+            col_space_value = f"{value}px" if isinstance(value, int) else value
+            self.col_space[column] = col_space_value
+            # GH 53885: Handling case where column is index
+            # Flatten the data in the multi index and add in the map
+            if isinstance(self.columns, MultiIndex):
+                for column_index in column:
+                    self.col_space[str(column_index)] = col_space_value
 
     def to_string(self) -> str:
         lines = self.render()

pandas/tests/io/formats/test_to_html.py

@@ -896,3 +896,59 @@ def test_to_html_float_format_object_col(datapath):
     result = df.to_html(float_format=lambda x: f"{x:,.0f}")
     expected = expected_html(datapath, "gh40024_expected_output")
     assert result == expected
+
+
+def test_to_html_multiindex_col_with_colspace():
+    # GH#53885
+    df = DataFrame([[1, 2]])
+    df.columns = MultiIndex.from_tuples([(1, 1), (2, 1)])
+    result = df.to_html(col_space=100)
+    expected = (
+        '<table border="1" class="dataframe">\n'
+        "  <thead>\n"
+        "    <tr>\n"
+        '      <th style="min-width: 100px;"></th>\n'
+        '      <th style="min-width: 100px;">1</th>\n'
+        '      <th style="min-width: 100px;">2</th>\n'
+        "    </tr>\n"
+        "    <tr>\n"
+        '      <th style="min-width: 100px;"></th>\n'
+        '      <th style="min-width: 100px;">1</th>\n'
+        '      <th style="min-width: 100px;">1</th>\n'
+        "    </tr>\n"
+        "  </thead>\n"
+        "  <tbody>\n"
+        "    <tr>\n"
+        "      <th>0</th>\n"
+        "      <td>1</td>\n"
+        "      <td>2</td>\n"
+        "    </tr>\n"
+        "  </tbody>\n"
+        "</table>"
+    )
+    assert result == expected
+
+
+def test_to_html_tuple_col_with_colspace():
+    # GH#53885
+    df = DataFrame({("a", "b"): [1], "b": [2]})
+    result = df.to_html(col_space=100)
+    expected = (
+        '<table border="1" class="dataframe">\n'
+        "  <thead>\n"
+        '    <tr style="text-align: right;">\n'
+        '      <th style="min-width: 100px;"></th>\n'
+        '      <th style="min-width: 100px;">(a, b)</th>\n'
+        '      <th style="min-width: 100px;">b</th>\n'
+        "    </tr>\n"
+        "  </thead>\n"
+        "  <tbody>\n"
+        "    <tr>\n"
+        "      <th>0</th>\n"
+        "      <td>1</td>\n"
+        "      <td>2</td>\n"
+        "    </tr>\n"
+        "  </tbody>\n"
+        "</table>"
+    )
+    assert result == expected